I had the same thing happen to a 482 when I added a 12" ParaLift jackplate to it. I was able to slide the winch tower forward about 2" move the boat up, and it solved the problem. Moving the motor back by the distance of the jackplate has thrown off your balance. If it were mine, I'd take the winch tower off and use a band saw or saws-all and cut it so that you could move it forward to mount in the remaining back two holes moving the winch tower forward by ~ 2". Now understand that you have modified it at that point, and any warranty just went out the window, along with liability protection if it fails. A bad swaying trailer is more of a danger in my opinion than a winch tower mounted by 2 3/8" bolts rather than 3. That's a risk I'd take.
The bottom line is you've got the get enough of the load back on the tongue of the trailer. Just to check, try pulling it with a cooler full of water on the front deck and see if it corrects the problem.