What is dragging? Is it the tail of the trailer? Is it the hitch?
Either way, I think adding a wheel is going to make the problem worse. The problem is that the wheel, itself, lowers the contact point at least another 2 inches, increasing the pressure on the system.
If the problem is that the contact point is in a depression, you can lay a pair of long boards across the depression to make it more level while pulling out. If the problem is that the contact point is a high point, you are pretty much stuck with what you are doing now.
Another route may be to add air bags to the truck that you can inflate/deflate from the driver's seat. Inflate them when pulling out to raise the rear of the truck, then deflate them when out of the driveway for normal towing.
