It seems that the project has just achieved functional completeness! In doing a little algebra study, I ran across a proof showing that the Min gate, Max gate, and monadic gates 2 (Is False), 6(Is Unknown), and K(Is True), form a functionally complete set. To put it simply, any of the 19,683 two-input gates can be formed from combinations of these five gates. Since I've already built each of them in the real world I can now rest easy knowing that, if the mood struck me, I could build any ternary circuit imaginable using only what I have already demonstrated to work {high-five!}.

If anyone is interested, the ternary (actually, any-valued) equivalent to Boolean logic is Kleene logic. There are other competing logic systems (who would have guessed!) but I'm following the naming conventions of Kleene logic because it seems the most sensible to me. Sure that's arbitrary. Sue me.