I couldn't find the Un-Du at Walmart so I bought something else that looked as good. It's called Goof Off. It worked like magic! I just drizzled it on the sticky parts and then stuffed a little cotton swatch in to clean. All the junk came off. It seemed to dissolve the sticky stuff on contact, first try. Great stuff!
So, I can quilt again! Thanks for your help with my problem, everyone who responded.