After finding a couple more posts on this exact issue (which different people seem to have different working solutions to), I was finally able to make this work by moving these options out of the controller-specific config and into the main retroarch.cfg

input_enable_hotkey = "tab"
input_enable_hotkey_btn = 8
input_exit_emulator_btn = 9
input_save_state_btn = 4
input_load_state_btn = 5

Now it only exits on select+start, as it should. However, this is not ideal because if I use a different controller, those will map to different buttons :(

Progress.