So I found a solution that I think works (at least for me.) I changed the entire configs.hdmi>daphne folder permissions to 555 and when I add a new controller, I get this error:
However it does NOT overwrite my current dapinput.ini file. I can't see anything else in that directory that it would need to write to anyway.
I tested all 17 Daphne games and they all worked and they all kept my controller configs even after configuring a few new controllers so I think this is at least a fix for my situation.
Thanks for the input everyone! It was helpful to put me on the right path!