What about the legs? You can have a very sturdy top and shelf but if the legs are not that sturdy, the vibration will travel to them. I built my own table a couple of years ago with a 1" solid wood top, 2x4 skirting and bracing, and legs that are 2" square the entire length, no tapering at the bottom. The shelf is from the same 1" solid wood with 1/2" bolts on each corner with nuts on either side so it is adjustable. Overkill? Well I am also a woodworker so not for me. Is it heavy? VERY! But it doesn't move or bounce either.
If you have a way to get a piece of wood cut the length from the bottom of the shelf to the floor, stick it under the shelf temporarily to see if that cuts the bounce. It will need to be snug. If it stops the bounce, you know there is too much "give" at the shelf area.
One word of caution about the rubber type shelving/rug stuff - I used some of it under my embroidery machine for about a year. I went to take it up and it was permanently attached to my table. I think the heat from my machine over that amount of time glued it down. I literally had to scrape it off with a paint scraper! I do not use that stuff anymore.