The league may have an issue with any mounts on their equipment. I wouldn't allow it if I were them -- not to be a jerk, but wouldn't want to risk you trying to hold the league responsible if there was any damage to your equipment, or more importantly, any damage to mine! Plus, maybe I misunderstood what you're doing but I'm not sure you'd get a lot of useful information from the camera placement area you're talking about.
I've looked at this a little in terms of football -- the real football (!!). If you check out the gear college football video operations departments are using (and these guys know what they're doing), you'll see a lot of high quality Panasonic (and probably Sony) video camera equipment. You can scale that down a little by going with something like this:
Panasonic 4K Video Camerabut, of course you're talking $2500 out of the gate without anything else. Something like this, however, would be more budget friendly and still get what you want:
Panasonic 4K consumerYou could go used and stick with 1080, but I would resist the temptation to use a DSLR or Mirroless (GH4/etc.) setup. Cameras take great video but this isn't the proper application for it. Same is true for the GoPro.
The above consumer camcorder is similar to what high school football teams will use to record their end zone footage at their games. Most will use something more professional on top of the press box. Keep in mind that their end zone cameras are 10-15 yards behind the goal post with a camera hoist that goes up 25 feet.
Here's a good video to watch:
Western Illinois Video OpsIf I were you, I'd not take my word for much of this and go talk to a coach in charge of their HS video operations and see what equipment and other tips they have. Some of them are probably using older equipment that you can get much cheaper than what the above prices suggest. Once you find out specific models, you can search B*H, KEH, and other suppliers for the used gear, or get it local on CL.
Really, your biggest issues are going to be where and how to set up the cameras. For that, I strongly encourage you to talk to the league folks. They may have a rule against video and still photos -- figuring weirdos will show up and use such footage for dangerous purposes. When you get that worked out, settle on a camera, get a good tripod or two and go to work! Don't forget the editing process.
