Thanks for the reply!
As far as how I normally control in OBS, I don't. This is the first time I'm trying it, since before, I would just manually switch if I was at the computer. So unfortunately I have no experience otherwise. I would use the keyboard and the Twiddler the exact same way I already am, meaning I would run into the same issue.
Which means your suggestion for unique hotkeys is spot on. My problem there is that to get unique hotkeys without crossover, I would need to either, say, find every use of a simple Shift+ hotkey and remove it from the computer, or I need to find a way to get every key I press to be mapped to a bunch of unique modifiers (perhaps all 3 buttons: Ctrl and Shift and Alt simultaneously).
This is where the Twiddler may hit a ceiling, I'm not sure. But if I need to use the 3 modifier combo, in the long run, I'm going to run out of Twiddler hotkeys quickly, since that would limit the number of buttons I can use. Looking through the forum, I've seen discussion about custom mapping the keys of the Twiddler, which I'm hesitant to do, but maybe that would be the right idea? Just add modifiers to all the keys?