When I lived in DC, I worked as a freelance museum specialist, installing art for the Corcoran Gallery of Art and the Smithsonian. Great job. Both museum systems used Globe Movers. I have no idea of the costs involved, but I pulled this quote from their website:
"Picture Crates are built with 3/4" plywood frames and 3/8" plywood sides. The crate is lined with 1" polystyrene board. Stretched canvases and gold leaf frames are covered with pH neutral glassine paper. Multiple pieces are separated by full size corrugated cardboard. Artwork with glass is wrapped with 2 layers of bubble wrap. This crate can be built to hold a number of pieces and offers excellent protection for shipping."
If you're interested, I found their site at
http://www.Globemovers.com.
The art we installed at both museums arrived of course as pieces of whole shows; I would think moving a single piece would be most efficiently done by you. Larger cities may list art transport/installation specialists in the telephone directory, or you could call the registrar of any local museum to see if there's anyone offering freelance service. They would know.
When moving art ourselves, we used an unmarked panel truck. You don't necessarily want the general public to know the value of what you're transporting.
As an aside, I have great Washington memories of unloading the Globe trucks next to the Corcoran, and having Bush, Sr's motorcade drive by, and him sticking his arm out to wave. What a great city.