I recently made some dollies for moving presses and type cabinets. They are designed to work with a toe jack, which is also shown in the pictures. Essentially you jack up the press onto pieces of 2×4s, going one level at a time, then when you are above the height of the dolly, you lift one side with the toe jack, remove the 2×4s and put the dolly under the press, and then lower the jack.
One of them has a slot cut out to accommodate the front foot on the Vandercook Uni I, which is also probably on other models, I imagine. I think it is there to make it easier to level.
I have not used them yet, but I have moved presses on just regular cheap dollies before, this just is maybe a little bit more stable and easier to use (I hope). It’s possible the location of the wheels should be a little different.
When I do use them I might also strap the press to the dollies, but that might be unnecessary. You could also attach 4×4s to them as well to act as outriggers. Again maybe not necessary.
If anyone is interested I can send them the layout and the hardware list, or post it here.