In my experience with my red clay here in East Texas, I always have to add a bucket, or several buckets of dirt to the ruts to make them go away. If you just work with what you have, it will always be a low area, and hold moisture that will lead to more rutting if you go through there again.
I dump the dirt, back drag it, drive over it again and again, back drag is some more in the other direction, and drive over it again and again, until it is solid.
I do the same thing when I remove a stump too.