Depending on how supportive your admin is, you might see if they'll let you leave after halftime on game nights before a contest. The optics of this might cause some headaches if the football team is not doing well and if parents aren't aware that you are leaving for a good reason. Just be sure to over-communicate.

Don't hold your breath expecting coaches to schedule non-district opponents that are closer. They schedule teams (or try to) that will prepare them for district. Sometimes that means you have to play teams that are further away. Along the same lines, I taught at a 2A school just outside of DFW. There were many marching invitationals that would have been much closer to us but we would have gotten slaughtered. Therefore we opted to attend small school friendly contests that were further away.

Best wishes and safe travels!