That is a tough call considering you are in Florida.
My experience with almost every business down there is they’re full of dishonest, incompetent, flight by night clueless yahoos who wouldn’t last a week in business up North. Not stating there aren’t good people there, there are, but the state seems to attract the dregs of America.
I personally would rent a small U haul truck and pack and move them myself. It's not that far a drive and the peace of mind knowing they'll get safely to your new home will be more than worth the slight inconvenience.