I purchased burner valve cream from The Old Appliance Club. The cream comes with some pretty easy to follow general instructions. They aren't specific to a Tappan Deluxe, but it's not brain surgery. I was a little intimidated to start this project, but once I had the valves apart it...I had an ah-ha moment when I realized how simply they work.
I used a mild degreaser to clean the parts. You just need to pay attention as you disassemble, so you can reassemable the relubricated parts the same way. My valves turned out well and now turn pretty effortlessly with a satisfying little click. I plan to have them professionally reviewed before I put them into action.
Of course, I started working on the valves themselves a while ago. They were covered in grease and the brass was a total surprise.