Testing the input with a known source like a mic is a great idea. Mind the signal levels when moving the cable to the F-1X!
It's absolutely correct that phantom power should be no problem at the F-1X end. I am wondering whether it could have an effect on the mixer input, though.
I'm going by the schematic posted here. It shows that the transformer in the F-1X does not have a center tap that can be grounded. Without a ground reference at this end, phantom power could cause the inputs of the mixer to float up to 48V DC.
This should not harm the mixer inputs (otherwise, they would be damaged if phantom power was on with nothing connected to the input), but since usually the use of phantom power means drawing current from these lines and thus pulling down the DC voltage, the inputs might not function correctly if they are being held near 48V.
We don't know what the input circuitry of the mixer is. If the mic inputs are transformer isolated, the DC shouldn't be a problem. But that's a lot of high-quality audio transformers (one per channel). If the inputs are directly connected to active circuitry (like op amps or transistors) without capacitors to block DC, they might not function correctly.
I'm really guessing here and trying to come up with testable hypotheses about where the problem could be. I don't think phantom power is a likely explanation, but it's not impossible and it should be easy to verify that it's off and eliminate the possibility of this particular problem.
