Thank you so much! That was the problem. For those who may have the issue in the future, I was using the variable names from a per-controller config (the one called LogitechGamepadF310.cfg). If you want to override these in retroarch.cfg for a system (or globally) you need to use the values that flipbug showed.

Mapping for the F310 is a little different than the F710, so I ended up with:

input_player1_joypad_index = "0"
input_player1_b_btn = "0"
input_player1_y_btn = "2"
input_player1_a_btn = "1"
input_player1_x_btn = "3"