Stripping may be easier than you think, use a heat gun and it should peel off easier. You could sandpaper the door facings down to the oil paint and then use a good primer before repainting with paint of your choice.

the latex will be fine

Amazing. The painter that painted the latex over oil without proper prep is obviously not a real painter so taking advice on how to remedy this from this guy is probably a bad idea. These days, it's not hard to paint over oil based paint with latex...all you need to do is sand it or clean it well before painting and use a decent product. It's guys like this that cause the general public to think that you can't paint over oil based paint with a latex. The purpose of PeelStop is to bridge areas that have peeled with areas that are still adhered. If your paint isn't stuck, it has to be removed. Putting any product over the top of paint that has failed isn't going to work.

House is 25 yrs old, guessing existing paint is 15yrs old. For short periods of the year, the shower is used daily, with fan, but as part of this renovation, we discovered that the exhaust fan did not vent to the outdoors, only to the attic. So probably more moisture than there would be ideally. (So we also are installing new properly vented fans.) Didn't clean walls with any product, wiped down. I spoke to Valspar this morning. They suggested I should have cleaned and lightly sanded walls, spot primed the mud. Regarding my concern over peeling, the rep said the paint can take up to 30 days to cure and that he would expect it to harden and adhere more during that time. Then to spot sand lightly where needed to repaint peels. I see now that I can't just go by what the paint label says, but the problem still remains - What's going to happen with this paint that is now on the walls? I have more painting to do, so I'll wash and sand the remaining walls. I can't put my whole project on hold for 4 weeks to see if this paint will stop wanting to peel, but I really don't want to have to strip it all.