Well, when I was getting my bath the other day I had an inspiration. I have this little glass spray bottle that I keep a solution of lavender diluted in olive oil in all the time. It's great for treating cuts, scrapes, etc, and lately I've been using it for little cheeks and noses after wiping them so much. It suddenly occurred to me to try it on my washrag, so after bathing I sprayed some on the rag and then "bathed" again, I even used it on my face. Let me tell you, it did the trick. My skin felt so soft and moistured but not at all greasy. And it lasted all day long, too. I will definitely be doing this again.
Just thought I would share that in case anyone else has the same problem. If you don't have lavender, I feel sure just plain olive oil applied to a rag while you're in the tub will do the same thing.