From seeing your pictures, and reading this last statement, I'm realy questioning if you can accomplish anything here. I'm also thinking that your contractor did as good a job as can be expected considering the distance and slope that he had to work with.
Here's the problem.
If you go in and get it exacly perfect. One hundred percent, dead on, it will still puddle on you after a few rains. It's not enough change in elevation over too long a distance to keep water moving. The water will carry small dirt particles with it and deposit them along the rought. The water will never move fast enough to create any erosion and carry the silt, or dirt particles with it. The result is that after a few rains, you will have areas that have more material in them, and they will create more of what you have right now.
My only solution is to raise the road and get it above the drainage area. Instead of spending $500 on a dozer, spend it on more dirt to build your road up higher. The further away it is from the water, the dryer it will be. You can't go down any deeper, so your only other option is to go up.
I have several areas like this and have had to move in hundreds of yards of dirt to get them up high enough to keep them dry. This past weekend, I received almost 7 inches of rain in two days and have learned that I have even more roads that will have to be built up. Digging down isn't an option as the water is already at it's lowest point. I have to go up. I think you have to go up too.
Eddie