The movers you want are the ones that are used by big organisations to relocate their people.

A friend discovered a nearly-ideal way to move out of the house they'd been in for >30 years: she trained as a minister for the Church of England, and when she was placed in a role the church packed up the whole house (including all the fossils and archaeological finds they'd accumulated) and relocated them.

That said, I've always hired a van for house moves, and it's going to have been a lot easier for me (never moving more than 20 miles since coming north for university) than for folk moving across the US.