Isolated audio without a transformer
Is there any reason this wouldn't work the way I think it would?


You cannot expect that circuit to work because the guitar signal ground connection has to connect into the op-amp circuit ground node and without that connection you are just going to get noise. The impact of this is that you are not therefore isolating the two receiver circuits as you previously wished would happen.

Try using fully differential amplifiers such as Instrumentattion Amplifiers but, don't expect miracles - IA's can isolate quite well but only within the voltage range of their respective power rails. In other words, if receive circuit A is offset from receive circuit B by a few volts to a few tens of volts you will hit problems.

True galvanic isolation (up to several hundred volts) is acheivable by using magnetics and therefore transformers.