With patience and and array of tools pretty much anything can be stripped, it may or may not be worth the effort. It sounds like your previous effort probably wasn't successful at removing all of the old finish, resulting in paint adhesion problems and easy stripping (you win some, you lose some). On the new cabinets you got very good adhesion.

You probably want to test a range of strippers. Usually time is your friend when stripping paint, so you want to keep the stripper from evaporating as long as possible. There are commercial kits to do this, but with some strippers it is also possible to apply the stripper and then wrap tightly with plastic wrap or polyethylene sheeting (something the stripper doesn't eat) so that the stripper can stay on for hours (overnight is good). I've had good luck with some of the citrus based strippers as well as nasty homemade mixtures that are undoubtedly banned. A heat gun is an alternate approach, or you can get the bulk of it off with heat and then follow with different strippers.

Once you get to clean wood (getting paint out of the pores in oak is a pita by the way), you'll want to scrub with a scotchbrite pad and the stripper that worked best, followed by a scrub with methanol or methanol/lacquer thinner 50/50 mix (outside with lots of ventilation and a proper cartridge mask) and then sand the wood to a like-new surface. In all likelihood your new finish will adhere nicely at this point. I'd apply a seal coat of de-waxed shellac to be sure and then an oil-based polyurethane.

This will be a *lot* of work, so painting might be a less painful solution. (btw, we've had great luck in scrounging very nice cabinets on Craigslist for minimal cost relative to new). To paint I'd follow the same stripping routine, but without worrying about using toothbrush and dental picks to clean out every crevice, sand the surface, prime with a shellac-based primer (eg BIN) and then topcoat with an oil based enamel. In my experience latex enamel over anything other than the proper primer is problematic, and you don't know what's on those old cabinets or whether you've gotten it all off.

One problem is that poly exhibits poor adhesion. In addition, 17 years of use probably got them pretty dirty with body oils, cooking residues, etc.

Latest paint is prone to "blocking" - meaning it adheres to itself and other things.

I would personally go with an oil based paint (with Penetrol, to help it to level out), assuming you are unable to spray (which opens up a number of other options). You can look for one that's "KCMA certified" but that's probably not going to be an arrow in their quiver. DO NOT apply poly over the top. It is unnecessary, and can cause more problems that it might try to cure.