"I would look into the t7i, and the TAMRON/Sigma 150-600 mm lens."
I like this suggestion a lot. Make sure you get the G2 version of the big Tammy. Next you will need to practice with it. It is big and beautiful and will do the job but you need to learn how to use it.
Some other suggestions might be to use Av mode. Set the lens to f5.6 or f8. Again, experiment with it and learn. Select a fairly high ISO, say >3200 but try <1600 also. (Never use auto ISO) Again, learn! Let the camera select the SS.
Noise in the shot may be or it may not be a problem. At any rate here is the most important part of your situation, get and use a good post editor. If you do nothing else, get a good post editor and learn how to use it. I would rather you get a good editing program than even a new camera/lens. It is that important. Most of them deal with noise well.
My last point and perhaps the most important point is made up of three factors. Well, I mean, lets say they are right next to a good post editor. What is it? It is location, location and location. Single most important thing is where you shoot from. All the guys that tell you exactly what gear to use fail to mention this most important point. Without knowing this one thing they can not tell you with any authority what gear to use. Sidelines good, bleachers bad. Being able to roam the sidelines fantastic. However, this makes the suggestion of the big Tamron such a good choice.
Modified recommendation, "I would look into the t7i, and the TAMRON/Sigma 150-600 mm lens.", plus a post editor and good spot to shoot from.
EB
EOS 1DX and 1D Mk IV and less lenses then before!
