Rick,
Sorry about the broken leg. If you can sit in the driveway (the truck), bring the RPM's up and nothing happens, then the problem isn't with the rotating mass of the engine and clutch assembly. You have already verified this...good.
If the thing goes nuts at low speed, my bet it isn't a tire. Does a 3/4 ton have a two piece driveshaft with a center support or center bearing? For something to shake as violently has you indicate, and a a very low speed, it must be way out of balance.
The driveshaft, if not assembled properly could fit the bill on the "whipping" at low speed scenario. If the rig was on jackstands, not under load, you might not get it to happen.
When your gam heals, grab a creeper and spend some time shoving and shaking on the drive train. Look for scraped paint where some support might have jumped around...you'll find it!
Stuart