We all know these enemies who don't attack in GAC until the last hour(s) and then may defeat you or not. I thought there might be a way to encourage these people to not wait till the end:
reward 6 points for every won battle within the first 6 hours
reward 4 points for every won battle within 6 and 12 hours
reward 2 points for every won battle within 12 and 18 hours
no points for fights in the last 6 hours
These points should go directly to the championship score, just like completing feats. They should not count to banners and give no direct advantage in the battle.
In division 4, for instance you have 4+3+5+2 = 14 battles and can earn up to 84 points. Over the whole GAC this would make 84*9 = 756 Points. Not so much that it would brake game economics and this is maximum possible bonus, if you can't clear all fields, you get even less.
This could encourage not to wait too long with attacking. A little balance between getting more points, that can make the difference to kyber, and waiting to see how well the opponents performs with his attacks.