I’ll use carb cleaner or brake clean for initial cleaning ie.. removing of any machining fluids, old grease oils etc. For final cleaning just prior to rust bluing I’ll scrub well with Greased Lightning .
Don’t think your problem is because of oils, you may want to allow your parts to rust a bit longer, different steels rust differently. I know with Winchester NI steel barrels I need to let them rust overnight. Also keep in mind that the WX has a lot to do with it, higher heat & humidity = quicker rusting. Colder temps generally means less humidity..
Just a thought
Mike Hunter