We ponied up about $4K to move from Blufflestank to Palm Springs. We packed it up ourselves and this was in October. However, we used a shady, fly-by-night service. I do not recommend this.
You are on the right track by having movers do an on-site estimate. You also should not sign a contract unless it has a "Will Not Exceed" estimate. But being the savvy shopper you are, I'm sure you know that already.
Remember, if you wish, you will have help unpacking in Phoenix. I'm sure both Debz and Randy will be happy to cart your crap around while you and I acquaint ourselves with the neighborhood Hooters.