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IMO........A-TRAC front and rear could be considered a simulated LSD
The Torsen CDL does distribute torque front and rear
I do have a Eaton/Harrop rear e-locker on the shelf... I still need find the time after all these years to get it into a shop as all the wiring and switches are in place for the install.
^ ... best to use Gear Oil that is not formulated for Limited Slip (LS) ... not adding value ... so best additives package would be non-LS synthetic Gear Oil.
Years ago, I had an Auburn front diff installed in my part-time 4WD 2nd gen 4runner. Most of the time, the 4WD hubs were set to "free," so the front diff/axle were silent. When I engaged the front hubs, whether t-case was engaged in 4wd or 2wd, the rig would want to track straight and had a slight "notch" when the steering wheel was centered, which I found bothersome. In retrospect, I would have rather stayed w/ the OEM open diff. (t-case was "locked" all the time whenever the 4wd was engaged)...easier to steer, as 99% of the time, I was in 2wd mode. After all that part-time 4wd fuss, my next two 4x4's have full-time 4wd.