I've had good experiences with ABF Freight, but it might not work for everyone. They drop off the back of a trailer at your place, let you load up, then you call them to pick up the trailer and tell them where it's going. They charge by the square foot of the trailer that you use, so there's some more savings there. They provide bulkheads that you use to seal off "your section" of stuff in the trailer, and they'll fill the rest with other stuff going to the same place.

Biggest downsides are that you need to have the space to put a 30+ foot long trailer (usually street parking unless your driveway is long and straight) for at least 2 days, and I would recommend that you have storage on the other side for your stuff even if you don't yet have a place because the one time that I had to pay their trailer storage fee, it was quite pricey. Also you gotta be flexible on delivery (don't pack anything you can't survive a month without) because occasionally, their drivers get rerouted or delayed.