I have an update on the flex plate. My friend was able to mount it on a tire balancer, and recorded this video showing it wobbling. This suggests pretty strongly that the flex plate itself is bent.
https://youtu.be/Zo2_0gSt0cs (in case that doesn't embed: https://youtu.be/Zo2_0gSt0cs )
So it looks like I'm in the market for a new flex plate again ($400 for NOS from DMC, it seems). My friend only tested the one, but the fact that both plates were wobbling in the same way on the engine concerns me a little. I'm not really sure how it would have gotten bent, or if I have to worry that, say, the torque converter is somehow damaging it. Obviously I don't want to get a new one just to have it bend again.
Thanks again. We'll be checking the oil pump out on Sunday morning. I hope to order all the new parts on Monday for installation next weekend.
-- Joe