Your problem may be your cleaning method. Nothing wrong with the hot soapy water, hot water rinse. But when that barrel is hot and you run patches down it, when they come out clean, then run a patch of alcohol down that warm bore. That should remove any residual water that is in there. Personally I don't care for Rem Oil. But use it if you like. I'd much prefer Hoppes gun oil or better yet, Montana Extreme Bore Conditioner.
Yes, SOME oils will actually attract water. (motor oil for one). But your quality gun oils will not.