I'm writing this from my sick bed. It seems I have a lot of time to think right now.
I have always had about .004" to .006" taper over a 6" long cut. I have leveled my lathe but I have a theory why it may not stay level. This is a South Bend 9" lathe. It is mounted on a nice shop built steel cabinet bench with a top made of .125" steel. Where I think the problem may be is, this lathe is in a shed beside my home. The floor is 3/4" particle board sub-flooring on 2 X 8 joists 8 ft long. With the heavy machines, this floor has some give or "bounce". If I lift one corner of the lathe bench even .050" it throws the level out. I don't believe it is possible to keep things level on this floor. Now to my question. The lathe only need to be level to itself ( not the world. They put them on ships in a shop and the ship is not always level to the earth). Short of rebuilding the shop, I am wondering if placing a 40" X 20" steel plate 1/2" or thicker on the bench top and then mounting the lathe on the plate if that would help solve the problem of constant changing of the leveling. The lathe could be aligned to the very stiff plate and remain constant. Am I way out in left field in this thinking?
Mark, I think that you are on the right track by wanting to build a 'boat' under the lathe. However a 1/2'' solid steel plate would not be as stable as a 2'' laminated wood base. I would look at some heavy plywood (maybe the furniture making guys here could guide us as to choice of plywood) laminated to 2'' thick using epoxy. Then if the 'boat' needs to be moored to what is below it then a three point connection would be all I would use (like for surface plates). That way the cabinet and floor are free to twist and warp without stressing the lathe.
Once the lathe is aligned in all its parts there wood be (pun intended) nothing to upset it.
Trying to reinforce the floor is akin to trying to freeze the ocean so I would not go that route.
I hope you are getting well and will be back in your shop soon.