I also pipe a secondary/supporting DAW's HDMI out to a 65 inch LCD TV in the playback/rehearsal room, under flown 250 watt stage monitors, using a 30 foot under floor HDMI cable, no issues
Being a listening area, as opposed to being used for mixdown/mastering, I'm able to use lesser quality audio chain components. Multiple DAWs throughout the facility feed HDMI to this area, and audio is obtained thru both RCA effect send outs on the LCD unit, as well as discrete underfloor balanced cable home runs. These all, plus separate DVD and BlueRay players feed a consumer grade 16x4x2 mixer w onboard effects, dedicated GEQ, and the power amps. Rehearsal with any recorded video or audio, or even near realtime collaboration via Skype is a snap.
I can feed both audio and video in the reverse direction as well, to the 3 tracking/mixdown/mastering rooms, but at this point the consumer grade components in the rehearsal room become a liability.
For remote DAW control in this case, I use wireless mice. Up to 40' range, and I walk to the DAW console if typing is required. All my DAWs handle multiple simultaneaus mice, wired and wireless, without issue. I'm going to attempt adding wireless keyboards to the mix, but there are two modes of potential problems, distance and keyboard conflict.
Will update when possible.