Our Gen I's have an element of "play" in the drive-line as well. As this Viper is new to you, I would suggest that you and a Viper Tech put it on a lift before you buy anything. Check out all that has been suggested above, and take a good look at the diff to be sure that it is bolted down securely.
As GTS Dean suggested, be sure to check the sync on the two throttle bodies...as the left should lead the right by a small amount. Your car may or may not have had the TSB fix for this (evidenced by a small screw thru each cable adjustment button)...but even if this fix was done, it may need a readjustment as the cables age. At the same time, be sure that you can see the TB's go to WOT upon full pedal depression (takes 2 people). If this adjustment is off, aggressive driving cycles alone will not cure the "bull hunching" commonly seen on these models.
As an aside, over the many years that I have owned/operated/serviced/enjoyed our Vipers...AND have been reading/posting here...when GTS Dean posts, I ALWAYS listen as his experience if long and broad with these cars as well as with far more complex machines!!
Please let us know what you find is the problem and solution.