Over the years I've reworked a number of driveways that sound like yours.
I always rip out the grass with either a rear blade or box scraper. The box scraper usually works the best (you don't need the rippers down -- bet if they are turned upside down). For the first few weeks, it will look awful. With a little regular maintenance it will begin to look pretty good, and it will stay in good shape.
I'm not too far from you, and we are getting a nice gentle rain today. In the next couple of days before it dries out, get the box scraper level -- left to right.
Run it down the middle of your driveway to pull out much of the grass. Keep the scraper raised just enough so that the dirt falls away under the left and right sides of the box.
Then adjust it so that the left side is about 2 inches higher than the right side (ditch side). Make a few passes on each side of the driveway to move the outside dirt back into the middle. This will begin to build a crown.
Go over the middle one more time, with the scraper level -- left to right. Now drive on it until the next rain, and repeat. Do this a few times over the summer, and your driveway will look great.
The grass you dig up now will disintegrate. The rocks will form with the mud and dust to give a good hard surface.
Good luck,
Knute
