After digging around in the Ableton scripts for ATOMSQ, in the hopes of answering my own question above, it is indeed possible to light the controller's LEDs via MIDI, and consequently use the unit in a custom control configuration, while still using the "firmware" unit's functionality where desired - the "Inst" mode comes to mind as something that works well enough as is without needing to recode it entirely.

The trick, in a custom Ableton script, is not only to send the midi.NATIVE_MODE_ON_MESSAGE, which allows communications with the unit, but also use functions to turn off self._elements.lower_firmware_toggle_switch and self._elements.upper_firmware_toggle_switch for any relevant modes that might want to customize use of all the buttons/pads. The "lower firmware" buttons are the pads/keys, the plus and minus buttons and the A-H bank buttons. The "upper firmware" buttons surround the display. It's too bad that the A-H bank buttons and the keys are linked together, as I can imagine modes where I'd want to keep the lower keys as set up in another mode with the plus/minus buttons as octave keys, but free up the A-H buttons for other things. Ah well.

It's also pretty straightforward (if you consider digging through the decompiled python scripts straightforward) to control the display and send it custom text.

This discovery makes the AtomSQ much more interesting for me as a customizable controller. If anyone else was wondering whether it's possible to take more control of the controller via custom scripts, then hopefully the above is somewhat helpful, and can steer other tweakers in the right direction.