WTF! I have used Team Viewer at work - I had no idea it could work with a LAN connection and also had no idea it could support mobile -> PC! Have just played with it and it works really well - practically no latency - and that was going via the web. Unfortunately their iOS app doesn't support touch gestures (the Android app does) - so moving faders isn't as nice as it could be which is a shame, but this is definitely something I will bear in mind.
You are right - the reason for needing this is that the laptop is plugged in at the rear of the stage usually and not easy to get to - and the perspective I'd like to have would be FOH.
Thanks for this.