How about a "vote diversity score" that accumulates over time and increases rewards if higher and decreases them if lower. Could help to get people to spread out their votes to new and neglected users.

I think we should mainly strive to improve curation, not just voting diversity. These aren't necessarily the same thing.

How about an "engagement score"? Post engagement (comments, replies and comment upvotes) influences payout.

That's too easy for a bot to game with automated comments.

How about another thing where someone who is first to discover and upvote a high payout post (by an author who has never had a high payout) gets a BIG reward.

This is possible, but computationally more difficult. And it's probably very gameable too. For example, a scammer could obtain a lot of "fresh" accounts, then obtain enough voting power to upvote them to this "high payout threshold" for an out-sized reward.

Even better. How about just random big rewards from the blockchain to a couple of posts a week.

I think we have some of that now. But the problem with that is while it might excite the author, it's bad for a system that displays content to users based in part on payout amounts.

While we're at it, can we finally add longer payout periods?

I know the Steemit devs claimed there were performance reasons to avoid this. I haven't had the chance to look into it yet and see if there's ways around it.