I suggest you run it from the line-level outputs on the back as they should be cleaner than the headphone ones. I have no experience with this unit, but perhaps you can can configure the active outputs on the PC and then it remembers which ones remain active and you don't need to have the PC connected from that point on. Or perhaps by default half of the outputs is set to the left channel, and the other half is set to the right channel. Consult the manual.
The outputs on the back are balanced outputs, so you get one channel per plug, unlike the headphones where you get 2 channels per plug. Something like
this adapter should work for both the headphones in the front and line outputs on the back. You will need 2 of these for the back connections, leave the right (red) in the air for both and connect your amp's L/R to the white connector (or black on this particular one) on each. For the headphone output just use one adapter and connect amp L/R to White-Black/Red as usual.
Of course if your amp has balanced inputs you could just use those with TRS to XLR cables from the rear line outputs, this would be ideal.