I used my own shipper as well. At the time a PT suggested 3rd party worked out better than the original PT quote, and better than u-ship.
But, yes, small freightloads are a pain- for everybody. Try u-ship and be patient. If someone is going by Tazewell, and your place, it won't cost alot, but given the price of diesel, and the fact that a bunch of shippers have gone out of business, I wouldn't expect to do much better.
And careful of depot to depot- my PT came that way on a semi trailer that ended up being too long for 'my' depot. The depot came through for me (for which I remain very, very grateful) and found an empty lot nearby, drove their heavy duty forklift over and unloaded it. But we were five pounds away from the load limit on the fork lift, so it nearly didn't happen.
All the best,
Peter