oh, your using a desktop... There are a few ways to solve your problem. First is to get multiple capture cards installed. I've had 3 BM intensity pro cards in my desktop machine, they are all controlled individually, and can be seen as individual camera's. This is probably the best and most versatil...
this can be done using the Resolme composition controls. (position X, Y, and Z) Your computer will see the 3 screens as a width, but then tell Resolume to use them as a stack, it may give you trouble if you're trying to use advanced output controls, or edge blending. It's been years since i've done ...
is it possible to use the record button with a live input? if so, then this feature already exists. I've never tried this before, so if it's possible I think i just found a nice new tool!
What I've done on the past is to send all my camera's into a video mixer, then capture the mixer output. It might not do what you want, but it's fairly inexpensive if you've got an old V4 laying around...