It’s easy to start ‘chasing the theory’ on this one. What I mean is you think you need a perfectly massive and stable mounting for your lathe. Whilst stability is good for obvious reasons that once installed your lathe needs very little further attention to alignment and mass can help to damp out vibrations so as to limit chatter issues it can be far less important than you think. I once realised that my Super 7 had been in use for several months with the nuts on the mounting block studs loose without any loss of accuracy or performance.
The lathe bed is a fairly massive casting (OK not anything like as massive as much bigger lathes) but compared to a flimsy wooden bench the lathe is more likely to deform the bench than the other way round. Move to a very heavy steel structure and yes you can get the bench to twist the bed if it doesn’t provide neutral support to the lathe (hence the jacking screws to adjust the support for each ‘foot’.
Leaving aside the supplied cabinets from Myford which are perfectly adequate to the job the advice is to mount on a sturdy bench and I would add that mounting blocks with jacking screw adjustment is at least desirable if not downright necessary.
Obviously the bench must support the weight and further to that should be reasonably stable in as far as not changing shape too much or too quickly. Wood absorbs moisture from the air and swells or shrinks accordingly so if you make your bench of wood then a good varnish all over will limit this. Joints need to be glued as well as bolted or screwed (unless you are into mortise joints) and the intelligent use of cross braces will resist twist. A symmetrical design will ensure that any movement of one half of the bench is balanced with a similar movement from the other half. Mass may help with vibration but the lathe does most of the work in that respect.
The aim is to support the lathe without introducing any stresses into it so I would say then that a badly designed sturdy bench can be worse than a lightweight well designed bench.
To return to the OP. He says his stand is sturdy but not stable over the long term. I would suggest that an alternative to starting again with a new stand would be to address some of the issues with the existing stand. Painting to stop moisture absorption and the use of either cross bracing or sheet ply to fill the sides which have the same function and will stiffen up the structure.
I hope this helps.
regards Martin