Maybe look into PipeWire, Reaper in jack mode works fine connected to PipeWire for me, without any of the problems you mentioned.

It is quite possible that your desktop audio already uses PipeWire depending on your distribution, you would need to look at latency settings if you want live playback.

A lot of fun so far ! Thanks for making this

Open source Not […] allow […] commercial applications

For some definitions of open source, this is contradictory (FOSS). Some non FOSS licenses do limit commercial use while making the source available, this could be a possibility for you.

But, I’d instead recommend that you check if a copyleft license such as the GPL provide enough protections for your use case.

I don’t have the information regarding xmodmap, but here are two other options which I am using if you are interested.

• With the compose key set, you can hit / = to get ≠. Or you can set custom sequences in .XCompose, but I don’t believe you can get the exact combination you suggested.
• Use a virtual keyboard manager such as KMonad