I've not shot anything at that level, but plenty of youth football. I'll suggest that it depends where you are positioned. If you are behind the end zone, or on the sideline up to about the 20 yard line, the 400 will be great on the 1.6 crop as the play approaches. When it gets close, you can switch to the 70-220. 300 will work, but I would actually prefer the 400. Less cropping when the play is far away, greater details as it approaches.
If by some miracle you can wander freely (I can do that at some youth games, I doubt you will have the same freedom at that level) then the 70-200 alone is probably all you need. If you can stay within 20 yards of the line of scrimmage, that's a great focal length.