Bob, Yes you can essentially bring the floor up to any height you would like. The design would take more steel and add more weight. The task of unbolting, separating, and inserting shims to do something as simple as leveling, when the option to build leveling screws (or leveling screws and hold downs), into a base design would, in my opinion, seem much simpler.
Yes that is what I did, my lathe came equiped with 4 tapped holes and jacking screws, plus clearance holes alongside them for hold down bolts, I welded up a base frame keeping it as square as I could, I have also fitted it with jacking bolts to set it square off the floor. Then I set hold down bolts into the topside of it.
When the base was set up flat and square on the floor, we lowered the lathe onto the frame, then using the jacking screws and hold down bolts to bolt the lathe up square, so it is now not only square, but also much more rigid as the base frame is now part of the lathe..
Using shims is a more painstaking process, but when done properly is just as good. normaly shims are only used in a factory where the lathe would sit directly on a concrete floor, the hold down bolts will be set in the concrete, either when it is poured or later by drilling holes and setting the bolts in with rock bolt adhesive. It is more difficult to set steel plates in the floor for the jacking screws, but it can be done, this why shims are often used.
When I was an apprentice I took part in this process an many occasions as the factory was enlarged and existing machines were relocated,and new ones installed, it was a great learning experience.
I gather many hobbyists in USA have timber floors in the shops, In this case it is essential to make a rigid frame for bolting you machines to as the timber floors will move and put undue stresses on the machine frame and it will never be square.
I did take some photos, I'll have to find them and post them.
Bob.