I don't have any good ideas on websites or channels where one can request such collaborations.
Insofar as this is posted to MO meta, there seems to be an implicit question as to whether or how MO could be used to promote such an inquiry. Realistically I think the options for this are a bit limited. Two things come to my mind (aside from the well-intentioned suggestions made by the Masked Avenger).
The first is to construct a good and well-focused question that involves your idea, and (maybe) to add somewhere in the body that you would be open to a possible collaboration on this, giving suitable contact details. (Or, you could bring up the prospect of contacting someone offline in a follow-up comment, if they respond usefully.) It is quite true that MO has some success stories where collaborations began with an MO question, and I think the community might be sympathetic to this. But the emphasis here would be on the question itself, and I think it would also be good to be low-key about the possible collaboration.
(There is sometimes a funny dynamic about proposing collaborations, not unlike the dynamic seen on sites like match.com, or so I would guess. Indeed a mathematical collaboration is a type of interpersonal relationship with someone you might not know too well at first, and which involves a degree of give and take and some degree of commitment and so on. People often want to weigh all sorts of factors before "taking the plunge". Same with how one chooses a PhD adviser, come to think of it...)
The other option, which I expect would be riskier in terms of the question staying open, is just to ask an advice-style question pertaining to the mathematical profession, which one sometimes sees on MO. You could maybe ask something very similar to what you ask here, or you could ask how other people in the profession broach the subject of initiating collaborations, etc. Such a question could be Community Wiki, and maybe such a direct approach would garner some useful suggestions. As I say it's "riskier", but as my dad used to advise me, "nothing ventured, nothing gained". Could be others are in a similar situation and would be interested in such a question.