I’m.not clear on what you are intending to do with the stand? It sounds like you intend to use the one frame and swap machines onto it, is that right?
If so I’d just make another stand, much less trouble. If not why do you need to move the stand round, my major machines are all static.
Also leveling a lathe is a bit of a misnomer, lathes on ships and submarines could never be level in the sense of a spirit level.
But they are set up to turn parallel which is the most important thing for any lathe to achieve accurate results.