[Roy Dennis]

I must say you do complicate things

Regarding the part of switching displays, the reason the displays have to be reset is down to Windows, those cheap switching units have to disconnect the HDMI feed from the computer your switching from and Windows then sees it as disconnected so reverts back to single screen. The only HDMI types of switchers that I know would work are quite expensive something like this: http://proav.roland.com/products/v-1hd/
The cheap way.
One question, does your projector have a composite rca video in ?
If it does then you can use a mini HDMI2AV converter, one from each computer. (cheap as chips on ebay : http://www.ebay.co.uk/itm/1080P-HDMI...MAAOSwdpxUVNRL) When you connect these converters to the HDMI output from the computer they register to the computer as being connected all the time even if the output rca video is disconnected from the extended display.
Next you need another cheapo RCA video switching unit such as: http://www.ebay.co.uk/bhp/rca-switch

Run the video ouputs of each mini converter to the switching unit then an rca video lead to the input of the projector.
There you go all for less than the price of a night out.
Alternately are you sure the videos you play in karaokanta are not playable in Hoster ?
Read my private message.