Forming the nylon petals for a spherical curvature, without stretching, crumpling, or melting them in the process, doesn't seem to work.  I think I would have to form them in a mold to do what I want here, instead of just rubbing them on a lightbulb.  That worked great for PLA, but PLA gets soft rather slowly compared to nylon.  Nylon pretty much maintains its shape, right up until it goes liquid.  Not that useful here.

Skipping the pre-forming, and just pulling them into that shape while retracting works, but requires way too much force for a little servo.  I'm guessing 15lbs of force over a 10mm of travel.

At this point I think I'm going to cheat and just go get some silk rose petals, and see how those work.

I'll probably still have to spring them with nylon to get them to open right, but the petals hanging up on each other, and not having the right curve, will at least cease to be an issue.