I believe that BTR recommended an oil change at 50,000 miles , unfortunately the oils you have recommended are not available here ,but I may look harder for the castrol syntrax .
I drove a couple of I hour trips yesterday day and the noise is no longer present once warm but returned when cooled ,
I have ordered friction modifier from Summitt racing which strangely varies from $9 to $90 for a 4 oz bottle ? And I will add a couple of oz and see what happens ,
The many different offerings state that it’s for “clutch type” differentials , Whereas the BTR is a cone type but the materials I would imagine are similar .
Btw the oil that came out was very dark but no visible metallic ie bronze in it .
Dave