Unfortunately an 1842 law requires single member districting. (Very little of the districting rules are in the constitution, in fact prior to this many states did send their reps via total state vote.)

The pie system I think gives too much recognition to the parties. Of course the parties are in total control under the current system, so it's an improvement, but I would rather remove all party control. Party control pushes for incumbency.

Indeed, I like a mathematical algorithm because it doesn't encourage incumbency. My system tries to limit it, but not completely -- that's a flaw balanced by the fact that I think you could get there from here.

A nice little essay I read showed the dangers of even convexity under party choice. Imagine a state with 2 districts which is mostly red on the north and blue on the south. If you divide it with a horizontal line, north from south, you get two safe districts. If you divide it with a vertical line, east from west, you get 2 volatile districts which swing with the undecided and independent voters. Quite a difference from a fairly aribtrary choice.

The house is the place where minority views are supposed to be a bit stronger, at least in states with 4 or more reps. If a highly environmentalist area wants to elect a lone green, it can happen -- and does happen in many countries. If the 2 dominant parties control it, this won't happen.