@mitu Before I considered dismantling the buttons from my arcade, I found this other command called jstest, which allowed me to see on the command line what each button was configured to on the USB encoder.
Once I ran jstest /dev/input/js0 for player 1 controls and jstest /dev/input/js1 for player 2 controls, Player 1 appeared to be configured correctly with buttons A and B. However, Player 2 clearly is the one not configured correctly. Here I finally found my problem where player 2 had buttons A and B setup to the wrong physical pins of the USB encoder.
Now that I had SW proof of my mistake, I disassembled my controller case and flipped the connections for those two buttons on player 2 onto the USB encoder. Put everything back the way it was, and behold my arcade is now acting correctly with both controls synced up.
Thank you very much @mitu for your suggestion. I do appreciate it.