Anyone know of a board that can control multiple camcorders?

wow, you are in the entirely wrong department of the video sales. you definitely do NOT want camcorders. what you want are the teleconference type PTZ cameras, they look something like "security" cameras but are a lot more sophisticated. they can be controlled remotely, one central console can work several cameras for pan, tilt, and zoom eliminating the need for an operator at each camera. The Sony model numbers are in the EVI- series. Cameras will cost about $400 to $1200 each. Controller for 4 cameras are in the same price range. you will also need to buy cable to interconnect and monitors to watch the pictures. This may be out of your price range, check with public school districts, they may have distant leaning/teleconference equipment surplus. I have seen these come up on eBay too for about half price.

Buying separate camcorders is a HUGE waste of money. Just buy regular video camera that you then feed into a mixing board. You really need to find a local friend that can help with this, because you're well on your way to blowing a huge amount of money on a set-up that shouldn't be that expensive.