A couple of things about this wonderful design. First I agree that adding weight, lots of weight, low on the bench, will make this more stable and absorb vibration. However, that foot rest will be something like 5 1/2 inches high and only about 4 inches from the vertical supports, which means it will hit you near the ball of your foot. That doesn't sound very comfortable. Perhaps you could mount the bar below the base and further out.
Another point. Even with double locked casters (swivel and wheel locked) your foot on that bar is likely to make the base move. So I'd go with two fixed casters under the heaviest end and the best quality swivels on the other end. Still easily moved, but more stability. Four swivels will likely be a bit less stable wheel base, and with all that weight on top, the center of gravity will constantly be shifting as much as several inches as you move it around.
Consider the possibility of making the outriggers at the base much higher, and cutting away space to recess the casters so you have maybe an inch of clearance between the floor and base and the caster projecting down an inch instead of the whole caster height. That way your foot rest and the center of gravity, can be lower.
This is a terrific design. Thanks for sharing it. Looking forward to seeing the finished piece.
The more I do, the less I accomplish.