should be fine to push in a stright line mind
could be brake bind or somthing else causing drag? sierra disc calipers are well known for been sticky when old
other options are to jack up the back and see if you can pinpoint the problem, pull out the prop to isolate the gearbox or drop out the drive shafts to isolat the diff.
my car i can push round easy on the flat and a lsd will ony effect pushing the car when turning
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