I use a moist towel to wipe off the soap scum during my shave and I have never had any problems. It is the same towel I use to prep my face and therefore it is wet. I just strop the blade after my shave, on a paddle in order to dry the edge. I seldom use oil before storage and I have never had problems with rust.
I can understand your frustration. If I were in your shoes, I would follow the advice in a previous post and get it re-honed. To emulate a paddle strop, I have read that you can put the strop on a table whilst stropping the blade.
Hope it works out for you, it is worth while persevering. Keep us posted on your progress!
"Nothing would be done at all, if a man waited till he could do it so well, that no one could find fault with it." John Henry Newman