First, use a penetrating oil like PB Blaster. Then break the nut loose with your 9/16" wrench.
I made a "screw driver" out of a Craftsman 3/4" cold chisel. I reshaped it to fit the oval slot heads. The shank on this chisel is a 5/8" hex, and is perfect to put a 5/8" deep well socket over...this is so that you can "carefully" use a 3/8" drive impact to do the work.
If you have someone helping you, have them hold the wrench while you "feather" the impact slowly. If no one is helping you, use the new vise-grip "nut" pliers.
Sometimes you will need to heat the nut and split them off with an air chisel if they are stubborn, rounded of from rust, of if the slot is messed up. Hope this helps!