V, are these plaster ceilings? I'm not sure what to tell you but the one or two times I've encountered radiant ceilings, cracking was an issue. Can't say I've ever seen widespread peeling of flat paint on drywall.
IMO, the popcorn needs to be removed, permanently. Repairing cracks on popcorn surfaces and fixing that finish is a huge headache. If cracking is an issue with radiant ceilings, you're looking at fixing it now and dealing with it again in the future. I would suggest, and Chrisn might be able to further this, that you actually line the ceilings with a wall liner and paint them. I've done jobs in Victorian plaster homes where extensive spider cracking made patching impractical, and the result was plaster walls that looked brand new perfect. There are steps involved in that but if you choose that route you can get the advice to do it here.
IMO, the popcorn needs to be removed, permanently. Repairing cracks on popcorn surfaces and fixing that finish is a huge headache. If cracking is an issue with radiant ceilings, you're looking at fixing it now and dealing with it again in the future. I would suggest, and Chrisn might be able to further this, that you actually line the ceilings with a wall liner and paint them. I've done jobs in Victorian plaster homes where extensive spider cracking made patching impractical, and the result was plaster walls that looked brand new perfect. There are steps involved in that but if you choose that route you can get the advice to do it here.