Karaoke set up

I'd like to set up my system to use it for karaoke. My problem is that I need to display the lyrics from my PC on screen while the sound from the PC has to go via the karaoke machine to the AV receiver. Only when the TV is displaying the lyrics, the AV receiver defaults to the ARC sound from the HDMI from the TV rather than from an aux phono input from the karaoke machine. I could just disconnect the HDMI between the TV and the AV receiver but is there a better way to get the AV receiver to play the sound from the karaoke phono output?

The bits and pieces are:

PC: Asus EeeBox PC EB1501P

TV: Sony Bravia KDL46EX503U

Karaoke: Lucky Voice Party Box

AC receiver: Sony STR-DH810

I was thinking of using:

HDMI from the PC to the TV

phono from the TV to the karaoke

HDMI from the TV to the AV receiver

phono from the karaoke to the AV receiver

So basically how do I get a Sony STR-DH810 to use the input I want?