Iím kind of surprised that the stain fixed the white spots since the wood was already sealed with the polyurethane. Oh well, I guess youíve got to take the good with the bad. 😀
Let others weigh in, but I think oil over water is safer than water over oil. To ensure good adhesion over the stain, I would make sure that the stain is fully dry and that any excess is removed. Poly is notorious for bad adhesion to subsequent coats,so donít give it any help. You donít want any film sitting on the surface that could prevent the next coat of poly from sticking. Iíd sand what youíve got to make sure it has some ďtoothĒ for the next coat to grab. If you want to play it safe, sand and apply a coat of de-waxed shellac before going back to poly. Actually, the original finish may have been shellac.