If you're not going to do it yourself, call Moore Security here in Houston to get a quote. It's a father/son company that is Liberty's Platinum dealer here in Houston. I bought a safe from them a few months ago and the owner was telling me he moves safes all over the state for previous customers and to ranches owned by people that live in Houston. From what we were talking about their rates were pretty reasonable. I've already talked to them about moving mine when I move and it's a $250 cost in the Houston area.
Being they are coming out of The Woodlands to BCS, you might be able to get a local rate. They have specialized dolly's and trailers to move it with, and the owner is going to move it himself with his own employees, most likely his dad, not a contract crew.
http://libertysafesofhouston.com/Honestly speaking, the last thing I would do is hire four laborers and rent a truck here in town to move it unless you want it stolen a week later....