Spring generally is the best time to move the tree. When trees are transplanted they need more water than normal and the added rain helps. Fall would be the next best time. Heat of the summer is the worst.

I have planted and transplanted Arborvitaes professionally in the northeast US. They do transplant well, however, make sure to allow for a big root ball. Maybe bring in a mini excavater (or small crew) and dig a trench all the way along them. That way you can move them all at once.

When replanting bring in fresh loam and use a plant starter fertilizer such as Roots Plus.