Laura, you could try Formby's stripper as it is supposed to allow you to remove a layer at a time--taking off the paint and leaving the varnish, shellac or whatever is underneath. But my results with this have not been too good. I much prefer Citri-Strip, which does take off all the layers. You will have to refinish completely but then you can apply the kind of finish that fits your needs. Be sure to follow the manufacturers directions and safety protections.Citri-Strip has a web site if you have questions. Being in a damp environment, you might want to consider a water based Poly for the final finish as it will allow you to set glasses on it without harm. Varnish doesn't like water.