How can I feather the edge between still stuck paint and the layer below? (Latex did not stick to gloss oil paint)
Ever do bondo work on a car?  That's pretty much it.  West System epoxy and various sanding fillers, interspersed with 24-48 hours to wait for the epoxy to cure enough to sand, and an exhausting amount of sanding, rinse wash repeat until it looks right.   It takes a really long time.  

The upside is this will also remove the wood damage, which is not inconsiderable. The downside is, it's really easy to mess up and damage trim with a power sander.