A dedicated drag car is not worried about putting 50,000 miles on the ring and pinion. Second a trailer queen is not going to see the same rear temps as a street car. Drag cars need only an initial run-in since they are driven short distances and heat is not normally a problem with proper lube and backlash allowance.
Driving the car normally to the track is a break in cycle. I am glad to see you see the light.
You do not use synthetics on a new ring and pinion because of the break in requirments.