Listen to all connected keyboards concurrently

My situation: I have a Logitech G602 which has a bunch of extra side buttons. Logitech's software won't allow me to assign those to mouse buttons 4 and up so I have them assigned to number pad keys 1 and up. My BTT is configured to respond to those depending on what app I'm running.

My need: I want to assign extra sets of shortcuts to those buttons. The best (if not only) way I know of would be to use a modifier key while I press one.

The problem: BTT seems to lack the capability to listen to modifier key presses on my actual keyboard along with these mouse buttons which simulate number pad key presses on whichever virtual keyboard interface Logitech uses. If I try to assign a shortcut with one of my mouse buttons while holding e.g. command, BTT ignores the command key and only registers the number pad key. If I export my current preset, manually hack the file to tell it to listen to the command key (by defining "BTTShortcutModifierKeys" : 1048576) and then re-import, BTT will show the command key symbol in that item in the list but it still ignores the command key when I try to use that shortcut.

Further info: I attempted to use the "Key Sequences" section to listen to 'command down' to switch to another preset and 'command up' to switch back to my main preset (along with defining an action in the secondary preset to respond, of course). it sort of worked - it initially did what I wanted but then things became laggy and also BTT wouldn't reliably switch back to my main preset when I wasn't holding command (meaning that all my regular stuff stopped responding). Even if it worked properly, I think it'd still be too laggy to be useful.

TL;DR I think it'd be great if BTT had some sort of option to combine all (or a selection of) keyboard-like devices into a single pool that it would then listen to for keyboard shortcuts.

If someone knows how I can do what I want in BTT's current state (excluding separate presets), please tell me! (to other users: Keyboard Maestro can't do it either so please don't bother trying to suggest that)