So that was the "Failure" of this round (always an option) but I did figure out a few things. For one, I made this batch using roughly 1/8th the amount of water I usually would by "massaging" the pulp over the mesh rather than trying to float it. I like this using of a few cups of water rather than a couple gallons so I'll probably try to continue it. I also found that just leaving the paper out in the open to dry overnight, no covers or books or any such seems like a perfectly valid way to let them dry. There's some warping but not as much as I would expect. It may be relevant that it dried without being left out in sunlight, though I'm not sure.
Feels like it's time to do some further research.