Well, I quickly had success. Here's how I did it.
1. Spray with CRC Parts Cleaner.
2. Wait two hours and scrub with a Chore Boy copper pad. This quickly gets a lot of surface crust off.
3. Spray with the Goo Gone and scrub with the brown/course Scotchbrite pad. The green pad works but takes much longer.
4. Use the razor blade scraper to remove the thicker layer of contact cement.
5. Finally, give it a shot of parts cleaner and wipe dry.
I was able to remove the old vinyl covering to us as a template for the new material. The photo shows before and after.