Torsen diffs would work great with the Auto LSD. Humvees use the same traction control system but have Torsen Diffs NOT LSD Diffs.
By the way my 2016 TRD sport does Not have hill asst start. It's all heel and toe or gentle use of the hand brake...which applies brakez on both rear wheels .
Can you measure from the ground to the bottom of your rocks for me please.. Your truck looks way shorter then mine. I am still at stock height but have lots of ground clearance.