The question is getting close to two weeks old (after that it will no longer be displayed in community bulletin, which means that it will be noticed by less user than it is now) and so far nobody responded - if we do not count a few comments, most of which seem to be related closer to the question linked as an example rather than to the general issue the OP asks about. Let me try to address at least some points raised in the question. Of course, it would be definitely better to get some response from more experienced MathOverflow users. And perhaps also from moderators - since one of your suggestions was to flag for moderator's attention in the situation described in the question. So take this as a response of somebody who has more experience with reopen process and community moderating from other sites. Although MathOverflow is in some aspects unique, at least some things work in the same way as on other sites, so some experience from other sites in the Stack Exchange network is transferable.
What can be done with the already existing tools?
Stack Exchange software already has several features that help with reopening question. Maybe I should start by linking to the Help Center: What if I disagree with the closure of a question? How can I reopen it? and the relevant FAQ item: How do you reopen a closed question?
Reopen review queue. This is probably the most relevant thing for this purpose. There are several review queues, in connection with reopening the reopen votes review queue is relevant. Users with sufficient reputation can evaluate here some questions and choose either to leave them close or vote to reopen (or they can simply skip the review and leave the decision for other users if they are unsure). According to this answer a question gets into this queue if: 1. Somebody votes to reopen. 2. Body of question is edited with 5 days of being put on hold (the exact conditions can be found in this answer). 3. Question is "popular" (which is calculated using votes and views). I'd guess that the first two options are relevant for the situation you described in the question.
Users can check their votes and also recent reopen votes. Every user can check their past votes on their votes tab. In particular, they can check their past downvotes and their past close votes - and if they see some improvements, they can reconsider. (Either vote to reopen or remove the downvote.)
Users with 10k+ reputation have access to moderator tools where they can see recent reopen votes - they can have a look and if the question is worth reopening, they can also vote to reopen. At the same reputation level, users gain access to full review history. In particular, for reopening questions this means that a user can check which questions have been in the reopen review queue recently and for the ones that were not reopened, they can have a look and decide for themselves whether they want to add a reopen vote.
It is quite likely that there are not many users who actually do this. But your question can be considered as an encouragement to do this more often. (And, after all, it is not necessary that the same users who voted to close are the ones who vote to reopen. So if the question gets to attention to some other users, it still has a good chance that it might get reopened if it was improved.)
Reopen request thread. There is a reopen request thread here on meta. If the question is not reopened through the review queue and you think it should be reopened, it is very reasonable to post an answer there. This can attract attention of other users to the question. And the advantage is that some short discussion is possible in the comments - if other users disagree, they can layout their arguments why the post should not be reopened. (In the reopen review queue the users have to rely on what they see in the comments in the question. In this thread, the case for reopening can be presented more clearly.)
Separate chatroom? On some sites there is a separate chatroom with deals with stuff like closing and reopening. For example, SOCVR on Stack Overflow (here is the room's website where you can learn a bit more about it) or CRUDE on Mathematics (here is a short description of the room). Those rooms deal predominantly with closures, but you can find also questions that were reopened based on discussion in that room.
However, I do not think that creating a chatroom for this purpose would be suitable solution for MathOverflow at this moment. We are talking here about big sites, that have much bigger number of questions than MathOverflow and close votes review is almost constantly clogged up with hundreds of posts waiting for review. It is natural that in such situation users are looking for additional mechanisms to help with moderating the site (which includes closing and reopening) - but this is not the case here. And also, since those sites are bigger, they also have many users willing to devote some time to help with closing/reopening and other janitorial tasks. Moreover, with the exception of Homotopy Theory chatroom there is not much activity in rooms associated with MO so it is not clear whether this one would gain more activity than the existing ones. But if somebody feels that a room like that might be useful here, they can certainly create such room and see how it works out. Mentioning the new room in the designated thread might improve the chances that it gets noticed.
Should there be some kind of notification for close voters?###
Let me first point out that I have noticed in the linked example there is a comment of the form: "@username I guess, it got reasonably clear now, so I voted to reopen. What do you think?" (It was the username of the first close voter.) This actually does not notify the user (unless they already made a comment or edited the post). The only case when close voters can be notified is if the question was closed by a single user - which means either the first and the only close voter was either a moderator or gold tag badge owner's (the latter only in case of duplicates). There is a feature request related to this: If you put @username in a comment to a question, does it contact editors/voters? In order not to go too much into technicalities I will just add that links to some places containing the details on how to comment replies work can be found in the corresponding tag-info.
It seems that your main suggestion was to implement notification to close voters if the question was edited. There is a similar feature request on Meta Stack Exchange: Notify close voters when a closed question gets edited. Currently it is at score 43 (48 upvotes/5 downvotes). So if you feel that this is good idea, than you should upvote that feature request to improve its chances. (My personal objection to this is that it might result into having too many notifications. But I do not feel about this strongly enough to downvote the feature request.)
Is it useful to flag such posts for moderators' attention?
Well, probably it would be best to hear from moderators what they think about this.
The Help Center explicitly mentions: "If a moderator (user with a ♦ symbol after their name) closed the question, then you may flag it for moderator attention. Again, do this only after editing and include a detailed explanation of why it should be reopened. There is more than one moderator, and moderators do reconsider their decisions." But this is somewhat different situation from what you have described in the post. It seems that there is no clear consensus about this also among mods throughout the network, judging by the fact that this question has no answers: How should moderators handle a custom flag to re-open a question? There are a few posts which recommend flagging for moderators' attention only as the last resort after other options have been exhausted or directly advise against it: How to seek attention to reopen a closed question? or Should I flag my closed question after editing to receive attention?
It is also probably a matter of frequency. Let's assume that flags for this reason would be cast with similar frequency as reopen reviews. I was only able to find only four reopen reviews within a scope of approximately a week. (I found these reviews: 100908, 100784, 100675, 100641. Since I do not have sufficient reputation to see the reopen review history, it's a bit more difficult for me to look for such reviews. But I am still pretty confident that the actual numbers are not much higher.) Moderators would be certainly able to handle four more flags a week. But if we look, for example, on Mathematics, where number for reopen reviews per week are closer to 100, that would be IMO a non-negligible addition to the number of flags that moderator have to deal with.
My main problem with the suggestion that in such cases reopening should be requested from moderators is that on a good functioning site, the site moderation should be done by the community as much as possible.1 It is clear there are some situations where moderators have to step in. If a question is closed and reopened for the tenth time, or if some edit is repeatedly done and undone, they step in. They also deal with account suspensions for problematic users. And they do many other things which for us - the regular users - remain under the surface and we do not seen them. I think they should be helped by other users where possible.
Another issue is that moderator votes to close/reopen have an immediate effect. While it takes 5 votes from regular users to close/reopen (with some minor exceptions), a single vote by a mod suffices. Of course, a moderator has every right to vote to close/reopen if they think the question should be closed/reopened. By they probably still keep in mind that they can do this singlehandedly and are therefore a bit more careful with such actions. Here is what one of the current moderators said about this during 2013 Moderator Election:
I am of the position that mods should not be editors of the site. We have a considerable number of users with essentially the same powers as moderators with respect to closing/deleting/etc (except, of course, that mods votes to do such things is immediately binding) and it is they who should be doing the closing, deleting and so on.
As a mod on M.SE I vote, in fact, much less to close/delete/&c than when I was a `regular' user (It should be observed that a mod cannot turn off his modhood) and I restrict those actions to obvious spam and other matters which require immediate action.
1Let me digress a bit to say a few words about reputation. From the viewpoint of a user, perhaps reputation is importation as it brings gamification aspect and also user might enjoy that they can use moderation for bounties in hope to attract attention to some question. But for the site as a whole it is useful as a measure of experience of particular user with the site. Perhaps it is rather inexact measure, but it is definitely at least a reasonable estimate. Therefore it makes sense that various privileges are awarded based on reputation. And with them users gets more and more additional ways how they can help the site, if they are willing to do so. For example, it would not make much sense to put reopen review in front of a user who is here for the first day and thinks that question asking to solve $\lim_{n\to\infty} (\sqrt{n^2+n}-n)$ is a perfectly reasonable question for this site. Somebody who is at 3000 reputation points has already spent enough time on the site and is able to judge whether a question is suitable for reopening.