To connect the audio signals from all sources directly to the amplifier, but this has little to Toslink inputs. The Xbox 360 has absolutely no digital audio output even without Zusatzadpater.
Now go all HDMI sources in these switches, the picture via HDMI to the TV and the digital sound directly from here in the AV amplifier. All problems solved optimally.
The only restriction: This Umschater has not automatic, you have to manually switch with remote control. But that's not so tragic.