How large of a large tank are we talking?
More likely than not you will not find a large tank moving company, there just isn't enough business to specialize in that. That said, you have two options really, hire a moving company (one with insurance), and explain the situation, more likely than not you'll pay a premium based on the job though but it is a viable solution, especially if you get a contract that says damage will be covered by them

The other option is go to a LFS who might sell large tanks, and see if they have a tank maintenance company who can do it, as they will know the ins and outs of how not to move a tank (i.e. holding a tank by euro bracing, which a moving company might not know (but hopefully you'll be there to let them know)