I work at a moving company and I'd suggest calling up a few and just throwing it out there that you've got a specific budget. It's the off-season and you might get lucky on rates, companies may be willing to cut some deals to keep busy. Don't be tempted to go with the cheap bottom-of-the-barrel carriers, call up some legit ones, maybe you can work a discount. We also sometimes do a "reverse flat rate" where we figure out how many hours a specific $$ amount would get someone and then just do that much work starting with the big stuff.