A 2x4 jackscrew frame would be plenty sufficient, IMO.

I would still use a thick base since you don't want to flex the base at the same time you add pressure. How thick is thick enough to prevent flex? I dunno, but wood is cheap and I don't have to haul this around and up and down hills. I was trying to minimize the parts count and assembly tasks and still have the fundamental functions of the more complex fixtures out there.