I want to clean it all the way down to wood.
Taking off the shine would make it look better than it does, but I'm not sure it would make the existing finish feel better to me. I really do not like to touch the coating..I don't like the way it feels.

I thought I'd sort of approach it like a very large fingernail..and do the polish remover with cotton balls or something like that. I thought I'd work on small areas. I don't mind the tedious aspect of that idea.

I could slather stripper easily enough. It would be faster and less work.
Maybe I'll run a comparison with both in conjunction with my tape-test. That would probably be the best way for me to find out what I think about all of it at once..