Well, I accomplished the goal, but far from minimally so.
The construction may be found in my paper "Limits of Rush Hour Logic Complexity"  that also considers oriented sliding pieces of just 1x1, that turn a sliding piece puzzle into a weird kind of maze.
However you do raise the possibility of longer-lasting computers in other harsh environments, specifically space. The Voyager probes work in part because the feature size of the components is huge (discrete transistors that are inspectable through a microscope and in some cases the naked eye). Such components are hard to come by these days. Micro mechanical devices might even be a superior approach. And for most space applications speed is not critical.