In case anybody googles this thread in the future, I thought I would just say that, depending on the nature of the diode in the circuit, the resistor values will not work well.
What happened in my circuit was that reverse leakage through the schottky diode going into a 1 MOhm resistance was more than enough to raise the voltage at the gate of the transistor and turn it mostly off. This led to all sorts of weird behavior.
If I replace that pulldown with a 10k, problem goes away, as the gate hangs near zero and the transistor stays hard on. The extra current through the resistor wastes a bit of power, but this only happens when the external power is applied, not from battery (well, except for that reverse leakage through the diode.)
I love mistakes that I can fix without changing the board.