Bill,

I believe your move is somewhere in the range of 600-700 miles (depending on where in Tennessee you are moving to), and its on a way to Dallas, a route often travelled by moving trucks going from the east coast to the west coast, so you might consider hiring movers not necessarily located in DC (for example, some Texas movers might have long distance trucks in DC area retuning from deliveries in New York ad New England that could pick up your shipment).

Your budget is good enough to hire a more expensive company (for example, some companies that you should avoid would quote you around $0.45 per lb), so try contacting larger van lines and get quotes from their local agents in DC.