I am attracted to Vidit's idea of (as I understand it) an alternate, software generated, front page, best.mathoverflow.net. It would be something like the "Top new questions this week" in the MathOverflow Weekly Newsletter, which are also software-selected and are pretty representative (it's the "Greatest hits from previous weeks" that does not show MO in its best light). But it would be continuous rather than episodic. Perhaps "Top (new?) questions in the last 24 hrs." One could exclude tags like soft question and career (which would remove "How do you not forget old math?"), exclude those "[on hold]," those not yet tested by some threshold of views, etc., etc. Over time the moderators could adjust the culling filter to remove the chaff and leave the wheat of MO.
If there are insufficient visits to the alternate URL during a trial period, the experiment could be abandoned.