For good lube I remove any casting flash and parting lines from the inside of the carrier housing and also smooth or relieve any potential dams between the axle tubes and the center housing where they meet. Coat at least the inside of the carrier housing with a coat of Glyptol.
Choose a gear lube based on what the experienced and successful racers are using.
The pinion rpm isn't going to be any worse than the engine rpm but the ring gear could be spinning at big numbers according to the ratio. This I assume is where your heat concern is focused?
I'm not a LSR guy as you know so I'm having a little trouble understanding where all that heat would come from in just 7 miles, ambient temps acknowledged. Is warpage a common problem for vehicles in that speed range?
