The fail and the fix:
After some research on the web, I took a shot at the cause and ordered the dual coil and main coil. They arrived in a few days. The videos are excellent, and the dryer is even easier to take apart than it looks. Takes about 30 minutes start to finish. BUT, after I replaced the coils and re-assembled everything the flame still sputtered. Fail!
I decided to clean everything before calling the repair guy. I removed the drum as before, and also took out the grey gas burner (two screws). There was a white buildup in the brass orifice on the gas valve. Gently, gently, gently I used a toothpick to remove the white stuff. It seemed powdery, and smelled strongly of that "natural gas smell." After the white stuff was gone I had a clean hole in the brass, about 1/16" diameter. Re-assembled everything and the flame now is strong and smooth. Fix!
We purchased the dryer new in 2002. My dryer uses Philips screws on the body and has four torx screws on the control panel.