Nothing so particularly crude as a dog house, and certainly not a part on the thing from
Now that I think of it, the plate bases used on hand lithography press beds might be of the right sort of design, as they have to absolutely flat, perfectly smooth, and free from warp after repeated exposure to extremely high pressures. At my alma matter (which I still do some technical consulting for), we'd have them custom ordered to spec, made from some sort of fiber-reinforced resinous plastic. Similar idea to Garolite, but with a much more visible reinforcement weave. Dense as hell, and they get the job done. Only time they get retired is when some idiot comes along and thinks they know how to lift and maneuver that sort of load, then it inevitably hits the floor and chips. They've started replacing them with aluminum, so that when (not if!) they get dropped, the dents can just be filed away.
Agreed, creating a flat plane that is completely free of warping is a very difficult task. Perhaps a different solution would be to make the baseboard from some nice wood laminate, and couple it to a vacuum easel with some sort of leveling mount. At that point, any deviation from perfect flatness should be inconsequential in terms of the optical system.
Speaking of lithography, another potential base material could be stone. Couple the column to a metal leveling base like the Durst L1000s and then put a slab of stone on top of that. Weighs the whole thing down, good dimensional stability, easy to come by. Might have a winner.