Polyurethane is bullet proof, it stands up to water, alcohol and is great on furniture. But, check the range of heat it stands up to. A couple of light coats dried for 1/2 hour between and a last wetter coat, no drips, will give you a long lasting shiny finish with Polyurethane. I have sprayed it for years on furniture and my MQ brass end plates.
From your description I would have thought stripping and shooting it again would have been the answer, like ssssly said. But since wax is much easier try it first. Wax can be removed with alcohol, better yet lacquer thinner. Don't do that inside!
Good luck, let us know what happens.