That could be, I tried lifting the front in first while my wife handled the winch, then tried putting the back of the tire up first.I have the same tires and it fits with the hitch there. Maybe with the hitch on you can't maneuver it into place correctly?
About two years ago I lost my key to the hitch but ordered a new locking mechanism with keys. You have to remove lock mechanism and provide a code that is on the hitch lock. Cost about $50