Your logic is perfectly good, so it is very likely one of your assumptions is wrong. Sorry that's not as much help as one would hope!
Is the interconnect good? Does it actually connect to the jacks at each end? With no shorts? Perhaps you could find a source of constant-voltage sine wave, and measure the output voltage between the balanced outs (should be 5vFS), from ground to each of the balanced outs, and ground to the RCA "hot". Repeat at every stage - DAC jacks, cable ends, connectors inside each target device, ...
Having seen a zillion of these kinds of question, I am confident you will find the answer eventually!