It may or may not be the LSD additives that are the reason for recommending that oil.
The Trutrac gears are not generally operating unless cornering (or during loss of traction) so if you have gear noise in a straight line it will be the crownwheel and pinion setup.
This sounds different to a diff whine, almost like your hearing something engauging & disengauging. cant hear it easily under under load, but the exhaust sound could be getting in the way of that.
For the cost of 1.5L of oil might give the LSD stuff a go out of interest?