91% isopropyl alcohol works. The paint won't just fall off after a short time though. I usually let it soak for a couple of days and scrape it off, usually with a small flat piece of wood. The wood doesn't make blemishes on the plastic. Then I use a stiff bristle toothbrush to get the paint out of the hard to remove spots. I use Tamiya primer on the bodies and it's very difficult to remove. When I get to that point, I sand it smooth and prime again.
A wise sage that taught me a lot about wrenching on race cars explained why it was a good place to buy tools. If you buy a set of "whatever" and one of them wears out from use, replace it with a really good one from SnapOn. Mac, Craftsman, etc. to . The rest will be good for occasional use.
Go get some Glad Press and Seal. Remove the cap and clean the lid and bottle top. Cut a small piece of the Press and Seal and cover the opening. Screw the cap back on. You'll never have a problem with stuck lids again.