For youth football, you can safely drop your shutter speed to 1/640 which is plenty fast to freeze motion at that level. I try to stay at 1/800 for high school but I have shot quite a few games at 1/640 where stadium lighting is poor. Photos below were both shot at 1/640 which does a good job of freezing motion at the HS level and will certainly be sufficient at lower levels.
For years, I have shot sports in manual mode with fixed aperture (as wide as the lens will allow, f2.8 for your 70-200) and shutter speed fixed as fast as possible while keeping ISO reasonable, ISO is set to auto. A lot of sports shooters use this setup now because it provides excellent results. Basically you know that you want the lens wide open almost all of the time with night sports and shutter speed has to be fast enough to freeze motion so fix those values in manual mode and let the ISO be the variable to set the proper exposure. The habit of shooting Av or Tv priority goes back as a habit to the days when auto ISO wasn't available (of course film plus the early generation of digital bodies).
Always shoot in RAW, you can do a lot of cleanup with the images in post that just isn't possible if you save them in camera as jpeg files.
I wonder if your lockup issue with the lens could be related to battery power? Is your battery pack new and a real Canon pack? When I was using my 1D Mark II, I tried using non-Canon battery packs because I needed them in a hurry. It seemed to work OK until I tried to shoot a sustained burst and it would lock up because the battery voltage would sag under sustained load with the third party batteries.
If you have IS enabled, try turning it off because this will significantly decrease power demand. When the lens is going through AF while also trying to stabilize the image, it is drawing a fair amount of power. I leave IS turned off on my lenses when shooting sports because the shutter speed is fast enough that camera shake won't come into play. My 1DX series bodies have no problem supporting the additional power drain but it just isn't needed for that type of photography and it MIGHT help with the lockup issue.
About the only time I use IS at HS games is when the cheerleaders or band want a high quality posed photo and I will turn on IS and drop the shutter speed way down to get the ISO as low as possible.
Rodger
You are welcome and I hope that you are able to find out what is causing the lock up.
Leaving in 45 minutes to head out and photograph the first HS football game in this area of the "COVID season". My soccer playing daughter will be playing her first game as the kick off / field goal / point after person.
She looked good in practice and can't wait for her first game. I am used to being on the sidelines with her in soccer, it will be different also having her on the sidelines in football.
Rodger
