Yel - that is exactly what we plan to do the next time my father in law comes to visit. I think it will completely kick out the vibration.
I've been using the machine the past two days and it is down to a minimum thanks to a floor mat in there but it's a hair too high so I'm going to look for a skinnier floor mat I think - or just lower the drawer 1/8"
i think if you got a piece of wood as thick as the space is between bottom of the top and the top of the bottom shelf{where the machine is ] and 4 carriage bolts ...you will have a small bump but out from the machine where the bolt is [they have rounded heads your fabric should not get caught on them ] and maybe one in the back of machine ....can't see how much room is there ......but that would make the shelf solid and not vibrate so much ...good luck