Which type of transistor (MOSFET or BJT) would be better to use for the longest battery life?
You are only going to be switching ONCE.

The MOSFet gate will be 10,000 picoFarad. You are in NO HURRY to charge that up.

If the gate connection is exposed to the elements, and to corrosion and pollution out in the elements, then both choices need to tolerate the stray leakage paths ---- outside the circuit.

If you can maintain a very clean gate wire, then you can use a 22,000,000 ohm resistor as pullup.

The time constant of 22,000,000 ohms and 0.000,000,010,000 farads is
2.2e+7 * 1e-8 = 2.2e-1 = 0.22 seconds.