Yes, the Motul should be fine, except it is a bit viscous for our IB6 boxes, which should not be a problem for you in your locale, and the high temp/very hard use you will put that transaxle through.
I am just wondering how the limited slip additive in the Motul will effect the synchro/blocker ring engagement, if at all.
I would contact Gripper,
if at all possible, and ask all of these questions, as well as just how much additive is necessary for proper clutch pack function.
(On RWD/separate from the gearbox axle apps, most usually run as little as they can in order to achieve full locking, and only enough to allow for no chatter if street driven, and in order to save the clutch plates from excessive wear.)