I tried various concoctions of lacquer thinner, paint thinner and acetone today, as suggested in some of the posts above. It worked really well for stuff that had damage to the finish only. I put some teak oil on afterwards. It looks really nice, and was MUCH faster than a complete strip down and refinish. Isn't it nice when something takes LESS time than you thought?
These solvents didn't work too well for stuff where the damage was more extensive. For example, damage that extended into the wood itself didn't look very nice after cleaning the surface with acetone or lacquer thinner and steel wool. It also didn't do much of anything to the solid parts of the cabinet frames (i.e. the non-plywood parts that were finished with a different material). I did get it to work on a small door, but that was only because I could cover it with saran wrap to prevent evaporation. Then it pretty much worked like regular stripper by lifting the finish as a wrinkly, gooey film.
So, it's good news and bad news. I've been introduced to a great new technique for the stuff that really shouldn't be stripped all the way down. But, it looks like I still need some kind of stripper.
Would someone who has the "Back to nature" stuff be willing to do a test? Please put a blob of it on a sheet of clean aluminum foil. Leave it out in the garage at a moderate temperature. Let us know how long it takes to evaporate and how much (if any) residue is left. There was a LOT of hard, white residue left by the 3M stripper, and it was kind of a hassle to clean out of the wood grain.