>> Hope someone here can pipe up and give you a fix for silicon before you attempt to refinish.
Silicone contamination is always problematic. If moisture is easily going through the existing finish as evidenced by the water ring problem, then silicone containing supermarket polish or dusting products is probably not just on the surface but into the wood also.
There is no 100% process that will totally eliminate silicone. Normally the best process starts with a complete stripping of the original surface using a chemical paint remover containing methylene chloride which is something said you don't want to do.
More risky is to first wash the surface with TSP or other strong detergent. Rinse thoroughly. Then use mineral spirits applied with a green scotchbrite pad. Before the MS dries, wipe it totally dry using lots of paper towels. Keep a fresh face on the towels or all you will be doing is spreading the gunk around. Do the same thing a second time. Now, very lightly sand with 220 paper.
Go to the store and get a couple of cans of Zinsser Spray Can shellac. Lightly spray the surface, let it dry and spray a somewhat heavier coat. Let it fully dry and DO NOT SAND. The shellac is creating a barrier coat the is intended to isolate any residual silicone that may still be on, or in, the surface. Once the shellac is dry, you can apply the first coat of whatever you want for a final finish. Only then can you sand the surface but be careful not to sand through the finish or you will have a path for the silicone to affect the next coat. This process will generally give you a satisfactory result.
