Help with corner weight and vibration

The car won't be even side to side. The entire drive line is not centered in the vehicle and if memory serves, it sits off to the passenger side. Look at the rear end pinion to be sure.

Either way, weight distribution is not the cause of your vibration.

I'd look at the drive shaft and find a third shop if they can't even weld weight on. You can put hose clamps on the shaft and re clock them to fine tune the shaft balance and see if it gets better out worse.