Hi Mr. 88
To answer or question more directly, my opinion is that the amount of signal degradation you would hear from your mains with the wiring scheme you have stated should be imperceptible. If you do hear a difference from your Focals, I believe you should be able to connect two pairs of speaker cables to each of the Luxman’s outputs and run one cable to a Focal and one to a sub bypassing the pass through circuitry in the sub.
The bigger issue to me is your selected crossover point. Crossing over at 80 Hz creates a lot of frequency overlap from two separate sources which should result in quite noticeable muddy bass, that I believe would be more than just a little difficult to fix. It is generally recommended in these situations when you are not using a high pass filter, such as a miniDSP in your integration, to set the subs crossover point at approximately the main speakers 6db down point, which in your case would be 31 Hz, which depending on what type of music you listen to, could leave your subs with very little to do.
You might find the below white paper useful.