RE: As a rule of thumb, the optimal voting time is before 5 minutes
When I first read your post (the first version), I wondered why you were using the reward formulas to determine the ideal time to vote.
Your dialogue with danmaruschak basically confirmed this. I have already tried to visualise the reward calculation in some way. Unfortunately, this is not very clear because of the large constant STEEM_CONTENT_CONSTANT_HF21.
Showing the changes of rshares after each vote would be very interesting. I see you tried that in your comment. I can't quite understand it yet.
To the question in your post, however, I would say that in principle it doesn't matter when you vote, but who votes after you. Above all, it is an advantage if very strong accounts vote after you. If nobody voted after you, your reward share would always be the same regardless of the voting time.
Maybe we can find a way to visualise this somehow.
For purposes of the reverse auction, the "time" of voting matters. For purposes of the curation reward curve, the "order" of voting matters. What @biophil demonstrated, and I parroted here, is that when you combine those two factors the optimal time (on average) has to be some time before the reverse auction ends.
It's been a good clarifying conversation with @danmaruschak, and I'm glad that we had it, but most of that isn't really relevant to the argument about optimal voting time (and neither is the late voting time, which I also included). I only included the 2nd section so that the rules would all be documented in the same place. (and I got it wrong at first, so maybe it would've been better to leave it out😉.)