I would recommend experimenting with putting the machine on different surfaces. Does the behavior change? What you're trying to do here is decouple the machine from the rest of the environment.
Yes, a shop table might be able to handle the weight, but is the problem the weight of the machine or is it the machine itself? Is it possible the machine has just a little wobble when it sits on a flat surface? Could it be the rubber feet on the machine not quite being right? Is the table itself completely wobble-free? Is the room's floor on a slab or is it on a framed floor? Is the top of the table perfectly level?
There are vibration mats one can buy, but the durometer of them is usually for a certain frequency range. Maybe the OP's machine has a resonance that's outside the range of the mat she/he bought, especially at higher speeds.
The OP has done a lot to try and address the vibration, but more info seems to be needed to understand why there is excess vibration since it can come from things other than the machine itself.