My idea is that their existing projector is not getting VGA, but component video through that VGA connection. It either breaks out to a 3-wire component cable, or is just run over VGA. I find it very unlikely that if hooked up to HD sources it is being converted from component video to VGA.
Still, you need to look at the full chain.
What sources are there (make/model)?
What connection is being made to those sources? Component video? VGA? Composite?
What A/V receiver is in use?
Is there a scaler in line between the sources and the projector? (make/model)
No offense, but 'high priced' customization companies should make it so that complex systems work properly and don't have long term headaches. The guys who know what they are doing come out and make a system work on the first try and then that system lasts for years. So, while you may be able to do them same, and you certainly could buy them a remote and program it, at the end of the day, they may have been using this system for years, and it still works well for them, which makes it worth some amount of money to have a truly reliable A/V system.
It should be noted, that an A/V professional who would come out to your home would tell you immediately why that VGA connection isn't working.
But, dig into it and let us know what connections are actually in use. Perhaps hook a component directly up to the projector.
Is there a HDMI cable in place between the head end and the projector already? What is the game plan to deal with HD video in a DHCP world?