Yes its got the LSD, at work now so I cant try in reverse but backing slowly or even going straight I dont feel it or its so slight ive never noticed, its only during turning even slightly and the harder I gas it in the turn the harder it shakes. Going straight I can nail it and nothing. Here is the info. you requested. Thanks
The TSB is 03-003-04. I found this at http://dodgeram.info/tsb/2004/03-003-04.htm
it says for models 2003-2004 (DR) Ram Truck...no clue what the DR means. But what is described there is exactly what I am experiancing.