Just last year I paid an Allied contractor $8000 to move a full house (including a bigass motorcycle) from Maine to South Texas. I did all the packing myself, otherwise it would've cost another ~$1500 or so. Expensive, but not as bad as I figured it would be since you can't get much more cross-country than that.
Do your due-diligence, though. Read reviews and get as many quotes as you can stand.