You know there's a very simple solution to this, but no-one wants to kill the goose that lays golden eggs.
There's (in my opinion) just too many games to be squeezed into too short a time.
Reduce the Premiership to 18 teams. Reduce the Championship, Division One, Division Two to 22 each. To soften the blow, add 14 from the Conference to the eight displaced for Division Three.
It's ridiculous that the Football league MUST finish in the first week of May as well, presumably to accommodate the play-offs, and that the Conference finishes this weekend - we're not even out of April! But I guess that's another issue.