I'm no expert, but I hate to pay someone to something I can do myself, even if not as efficiently or as well. If it were my land, I would box blade right at the outer edge of the rut, as deep as my box would cut, 20-30 feet at a time. I'd use the loader to push that fresh dirt into the rut to fill it in as I go. Within a pass or two, it should be level enough to box the whole area as flat as you'd like. Might take a little longer than with a big dozer, but hey, you get to play on the tractor for several hours, win-win.
Again, I'm no expert,it's just what I would do.
Again, I'm no expert,it's just what I would do.