take a look at this manufacture to handle your final video output to your LCD's.
http://www.audioauthority.com/
You can input 6 video "signals" with audio and send it to multiple LCD's out as far as 1000ft. per. Takes 2 CAT5 per output. I use this on sports bars.......very impressive.
Your issue on the "headin" side is a completely different issue. You might input your "group" of cameras into a 6 channel matrix swicher that has loop outs and then input the combined camera signal into the Audio Authority matrix switcher which then pushes the signal out to your LCD's.
The "loop out" on the switchers would allow you to run the camera into a DVR.......which keeps a record of the action. And also, the DVR can/will have some "Monitor Outputs" that you can input to the Audio Authority Matrix switcher..........if you buy the right DVR you may not need any 6 channel switchers???
My only issue with your question is......you want a 1080i end result. This means nothing if you are using Standard Def or lower inputs.........it's still standard def. BUT, with the above Audio Authority Matrix Switcher you would be able to feed "some" 1080i or higher camera's.maybe 1 or 2 per room..............and any future HD type upgrades would be easy.
The Audio Authority Switcher is high speed low drag..................and in a training enviorment it would kick butt........it would also do well on Superbowl Sunday!!!!!!!!