You're in the southern part of the transition zone. You can grow any grass there, but I believe the southern grasses would do better with your humidity. If you want to seed bermuda, then you are too late. If you want to use either bermuda sod or St Augustine sod, you can still do that. If you want to use a northern grass like fescue or Kentucky bluegrass, then you can likely still get away with that in your area.

That's a small area for a dozer. You could use a box blade on a tractor and be done in a morning. It's a lot more maneuverable than a dozer.

What kinds of grasses are growing in the pasture?

I am ignorant about most grasses, so I am not sure of the type growing in the pastures. I have no preference on these strips.

I have a tractor, but do not have a box blade with cutting teeth to be able to do it myself.

Where were you going to get a dozer? Maybe someone else around you has a box blade and knows how to use it.

There is a person about a mile from me that would charge me $500 to come and move enough dirt to cut the ditches out wider.