All of the possible solutions have been covered, I think. All of my stationary tools are on casters or bases with casters. I'd urge anybody with a tablesaw, particularly with a table extension, to bite the bullet and buy a commercially made rolling stand. I have the Delta model on my Unisaw. Ditto on what's been said about bandsaws being top heavy!

Quality casters, particularly locking ones, make a big difference. I've put casters which were not as substantial as they should have been on some of my lighter tools. I'll get around to replacing them sooner or later. The hefty ones are more expensive, but they lock much better and their "tires" have much better grip on the floor.

I think a lack of solidity is the price of mobility. The "lift" approach, which is how my heavy Unisaw is equipped, is best, since the machine is setting solidly on the floor when in use. For safety reasons, you really don't want a table saw going anywhere when you're using it! I have particular problems with my wood lathe and jig and scroll saws. The lathe has to be firmly set up to oppose the force of the pressure of the turning tools. The jig and scroll saws tend to vibrate excessively with the "up and down" motion of the things. I've solved these problems by rigging fixed wooden arms on the stands which permit tool to be rolled up against my heavy (and wheeled) main workbench such that the wooden arms extend over the top of the bench. I can then attach a couple of C-clamps to connect the arms to the bench top which provides a very rigid connection. Then the lighter machines don't go anywhere in use.