no room for any woodworking machines

total ht. of drawer ~~ 7.25"

re:*"between the cutter and the fence"
- do you mean to put the drawer in between the cutter and the fence??

Set up the distance between the very edge of the cutter and the fence to 7 1/4" and push through it against the rotation of the cutter. That means pushing from the left to the right if you are standing in front of the router table. the fence doesn't need to be straight with any portion of the table. It will always cut the exact dimension between the bit and the fence. Make sure you hold the drawer tight against the fence. Rub a little wax on the fence to reduce friction. How wide or tall is the drawer now? If your router does not bog down(1 1/2hp or larger), you should be able to cut 1/8" off easily with a sharp bit. 1/4" max. Any larger then that, I suggest making two cuts for chip or sprinter reduction.