Yes, the engines in particular those that are above 6 hp are vibration maniacs. I had an 8 hp briggs and dared not take it above 3600 before it vibrated like crazy. The balancing inside the motors is not terrific. One way to keep the vibration down is to look into your engine rpms. Is the engine screaming, or is just the thunderous pulses from the power stroke.
Cushion mounts help, but beware it will mess up your drive train. If you have the engine on an independant mount system, then the main hinge points can be isolated with rubber mounts. This will avoid the headache of mounting your engine on rubber mounts or spring mounts (like the paint can shakers you see at Home Depot).
The idea is to isolate the drive system/engine fromt he passenger compartment. I have seen that your tumbler kart seems to have this suspension system, so I would think it would be ideal to just isolate the suspension areas with rubber mounts similar to those cars use on their suspension components. (Remember most cars have rubber mounts on the bodies too...isolating the passenger compartment)
And finally...not to be overwinded... isolate your steering system with rubber mounts so the steering doesnt shake to death, and isolate the seat with rubber mounts, this will help keep the vibration down.
And yes one last thing, make sure your engine is tuned optimally and not running rich. Typically a rich running engine will have tons of torque but will have the side effect of vibrating alot. You can tell if it is running too rich if it will not run up in the rpm range without blowing black smoke and running rough.
GKG