The units that Don mentioned sometimes not even having computer inputs are more the consumer LCD TV type displays, but it is something you want to confirm. If the unit has a VGA input then I'm not sure why the LCD VGA inputs wouldn't work with most computer outputs. After all, isn't an LCD display what most people now use for computer monitor? Just usually smaller than 35".
One common issue is that most people run their computers or laptops as a 4:3 video format such as XGA and most LCD panels are 16:9 format native screens, so you either end up with a black bar on both sides of the image or you have the LCD display stretch the image to fit the full screen, which works to varying degrees depending on the display and the video image content. Perhaps that is what was being referenced, but you will have that same problem with any standard video sources anyways, including if you use an S-Video output for the computers. Or it may be that it was DVI inputs being referenced, although most LCD displays have both VGA and DVI inputs.
I had assumed that with the signal routing and multiple displays that there was some type of integrated control system that would already be controlling the displays, but it sounds like that is not the situation. That might affect which solution works best.
Before going the all S-Video or composite video route I would suggest that you mock it up. Using the S-Video or composite video output from a computer video card, routing it and then displaying it on an LCD display may result in an image that is not as good as really desired.