That cable might work. A simple check with a cheap VOM meter will confirm that it's configured properly if you know the wiring. The 1/4" connectors on the Motu are balanced connectors, so if there's no problem with the ground and shield being connected then fine.
You probably have a set of RCA cables laying around somewhere. I would just run the RCA to RCA connection, especially since both side go to the same point. RCA connectors have only been in use since the 1930s. They are pretty reliable.
BUT, if commercial music sounds right when played through your setup, then again, that means that the playback system is NOT the problem.