I still have my T2i!
Generally I will be shooting in our school's football stadium.
IMG_7289 by THGBrian, on Flickr
IMG_7234 by THGBrian, on Flickr
IMG_7188-2 by THGBrian, on Flickr
First two were shot with my friend's 70-200 mark ii and the last was shot with my 24-105. Anyway, I hope the pictures show how much the lighting varies at different times of the day. I'm not sure if I could get away with my T2i at 1/500. Plus, I wouldn't really want to carry that much gear around too....
I shoot some football and I would suggest not shooting from the stands or above the action. It resembles a point and shoot camera and doesn't take advantage of the shallow depth of field you have when shooting at f/2.8 and 200mm. So take your shots from ground level... take a knee because it is a slightly more interesting angle than standing, dont' lay down because if a ball or player comes your way, you won't be able to get out of the way.
Try and predict the future. Shooting the receiver jumping away from the camera is significantly less interesting than seeing the receiver jump towards the camera and you can see his eyes focusing on the ball. If you are stuck in one place... I understand... but if you are allowed to roam the sidelines... I like to spend time ahead of the action so I can see it coming my way.
Also... and I do this too to my dismay... if the action is happening on the other side of the ball, maybe you don't take that shot... because it is so far... and you would have to crop so much, but because of the distance, the depth of field is greater, so it doesn't POP!
As for the 70-300L... at an aperture of 5.6 at 300, you are losing 4x the amount of light that you might have at 200mm at f/2.8. And that's a lot when you are shooting night games.
and I still contend, that IS isn't important when you are trying to get 1/500 of a second shutter speeds or preferably 1/2000.
and I thought I said this earlier... but crop more. Isolate your subject... making them the only subject. The goal post and the bystanders... I would cut them out. and the group photo in the huddle... crop into the image and adjust your alignment a little... the blurring will be intensified and bring out the players a big more.
If you don't want a 2 body setup... I understand.
Are you allowed to use flash? Maybe a high speed sync using a 580 exii or a 600 rt? At a distance... there is a little less glare.
I still vote for the 70-200mm f2.8L USM (non-is) and a monopod. Night games are such a beech to shoot at f/4... even with the 6D...