My two cents are "ALL OF THE ABOVE" ...HAhhaa
Sounds like you need to slow down for sure; add weight on the table and/or machine; add a shock absorber of some sort (pad, mat, towel, etc) and maybe some weights over the 'arm' of the machine... sort of like saddlebags with sand or rocks or heavy nuts and bolts or whatever...
But with the table jumping around... heavy cans of soup (giant commercial sizes?) might help. Or get a sturdier table.Been there done that and that jumping is sooooo distracting and disconcerting.
Good luck.