Successfully modded my headphones to feature a detachable cable! Thanks @mawr for the suggestion and parts!
Downside is, apparently my cable w/ inline volume control only transmits mono. Dunno if that's a failure of the device itself or if it's a result of it being designed for one more conductor.
Hardest part was getting the ear foam back on. Also I reversed left and right channels at first but that was easy to fix.