I would think too that it's mostly the motor case that smells...disassemble, spray the peroxide solution onto the case pieces (not the coils or the armature) and let dry, rinse and reassemble. Might work. If there are any of the rubber grommets for the wires, or marettes change them out too. The plastic and the rubber will have soaked it up, and when they get warm.... yuck.
I had an electrical guy tell me to use brake clean.... it might work if the electrical motor spray doesn't. If nothing else, that brake clean should be able to overpower the other smell. It smells awful.
I'd probably do a double feature. motor cleaner on the armature, I still don't think I'd do the coils, or at least be really careful if they're the wrapped ones (like the singer motors) and then do the peroxide on the outside.
Maybe you'll find your "occasionally open circuit" too.