I had tried to simplify the Min gate with Wired AND but didn't get outputs that made any sense. I assumed this was because of diode voltage drop. It's actually because I was assuming that a Wired AND Min gate would use the same monadic sub-gates as the Wired OR version. Of course that doesn't work because the different logical connective (AND vs. OR) requires a different set of inputs to get the same output. Long story short, I needed to use monadic P gates instead of monadic 5 gates in the Wired AND version. I had simply misinterpreted the unexpected outputs as a hardware defect when the problem was really "between the keyboard and chair".

Now the Min gate can be implemented with only two LM319's instead of three. I'm more than happy to spend time on all these tiny improvements because I know that component count will be of paramount importance to my ability to build more and more complex structures.

Here is the updated schematic. Again.