Lee, I have the similar Wargo GH (geared head) Universal mill. Mine sits on a wooden stand, which in turn sits on a wheeled base I bought at the time to help me manipulate the mill around a small garage.
When I bought mine, Warco was out of bases. I was later delivered the next size up, and I wish I had your one. I have kept the wooden stand as it is a better height for me I don't like stooping.
From my experiences with the wooden stand, I don't think it's possible to destabilize 300kg of machine, even though there may be some wobble and vibration. Heavy stone structures withstand a lot, often even earthquakes. I look at buildings and marvel that they stand, yet I understand cognitively in which direction the forces are going.
If you can raise it up again, some rubber might kill the vibration, the wobble is due I think to the thickness (or otherwise) of the stand, but I don't think you need be concerned.
Bill