Have you checked your transmission mount and tail shaft to be sure nothing is broken?
Did you check the motor mounts? (both sides)?
Have you checked all of the body mounts to be sure they are tight?
Have you checked the frame 100% for cracks?
Do you have a pilot bearing/bushing in the crank? If there is one, is it any good?

What starts shaking first? I.E. Does the shifter start shaking first and then the body?

Does it drive fine even when you are running the same rpm that you are at when the shaking happens when you are doing a burn out?

Just a few thoughts off of the top of my head.