Basically it's solid it could be better, and I don't see this as a primary ssue anyway it could be a contributary factor: it's a small footprint mill with a relatively stiff flimsy base.
Fixed that for you.
You could probably not even bolt it down and it would be fine
Doubtful. Bolting down to a substantial foundation is a pre-requisite for many heavy machine tools to perform as designed – why do you think a lightweight hobby mill would be any different ?
It's the column-base joint that's going to be the issue, not the base to table is an assumption
If the plywood base has no bracing underneath, it could be that the mill is just sat on a diaphragm. If there is no brace, adding a 3"x2" stiffener fore & aft under the centreline of the mill base (long side down), glued & screwed could help, as could replacing the top raising section of plywood with a pressed concrete paving slab & bolting through the lot. Plywood is a lot more flexible than concrete.
Don't under estimate the value of a solid foundation – it makes a big difference to large machine tools with far more rigid castings than a hobby milling machine. If you dig around, you will find reports of users of similar style hobby machines to yours resorting to adding a substantial bracket from the top of the column to the building wall to stiffen up the machines.
Maybe look at some other aspects before fixating on complicated "work-arounds" for less-than-perfect construction aspects that I suspect will not yield the improvements in performance that you desire ?
Nigel B.