You are totally overthinking this. The cable does not power the sub at all, it just carries signal to the sub. It does not need to be heavy gauge, or anything special.
When REL states it takes on the sound of the amp, it is talking about the levels coming from the amp. If you have a heavy bass amp, the subs will be louder, vs a flat amp, that will give the sub a more mellow sound. It just mimics the signal from the amp to the speakers.
Doubt you will be able to measure any difference with different cables. However, I did just swap the power cable on my sub, measured a 1-2db increase in sound over the stock cable. That shocked me.
As said, just use the OEM wires for signal.