Update: Well, actually, before the update, I'd just like to say thanks again for the responses. They've helped me make some progress and in the long run it will make me a better bike builder, even if I don't paint 'em anymore.
Since the post I've done two things, make sure my hands and the resurfaced area of the bike are clean, and put a layer of primer in-between the old paint and new paint (technically, that's three things, anyhoo....). The recent success has probably been a combination of them all. If the primer doesn't wrinkle, the top coat goes on without a problem. If the primer wrinkles, I sand it down a little further and try it over again with the next coat being primer first, even if I hadn't sanded down to the original primer layer. Usually, the wrinkles won't re-appear if it goes this route.
My advice to anyone in the future who encounters this situation: wipe down the bike with a clean rag after sanding, and never be afraid to use primer...paint on paint might not cut it.