My family has used
Three Men and A Truck for our past couple moves and they don't seem to come with any of the usual headaches that some companies do (not responsive, hard to get a hold of, not delivering on time, etc.). It sounds like you just need help with the labor, which I think is an hourly rate rather than a total, but I'm sure they do that too. Might be worth looking at since they came in quite a bit cheaper than some of the other companies we looked at.