Your best bet is to very carefully pack your own containers (possibly with direct help from a local mover) and work with someone to deliver those between states and then carefully unpack the container on the other end (possibly with help from local movers). Problem is that you have to be moving from and to a place with space for the containers to be packed/unpacked, and sit empty or full for a while while they're getting picked up according to whatever schedule you can arrange.

If you're renting and can't accommodate this process, I highly recommend only owning things that you can fit in your personal vehicle or can sell on one end and replace on the other fairly easily.