1 ball per innings would help batsman, 2 balls mean the ball will stay in better condition for the bowlers for longer right?
I think edge size could be limited. It would prevent mistimed shots going for 6, and wouldn't restrict the weight of the bat.
Balls which are going for 6 off the edge of the bat would miss the bat all together in some cases. Mainly in top edges.
A far out option, restrict the accumulative width of the bats 3 faces (ignoring the back of the bat).
Say your bat could be a maximum acc.width of 6 inches (random number off top of my head), with maximum face to remain 4.25 inch. Want a bigger edge? Fine, but you've got to take some width out the face of your bat.