You can do this! The best time to transplant large evergreens is early fall or early spring. Prepare the new holes first. Loosen the soil around the sides of each planting hole and soak the soil before you add the new plants. Dig up the arborvitae on a cool and cloudy day getting as much of the root ball as you can. Lay plants on tarp or towel and wrap root ball to keep soil intact. Immediately place into new hole (remove tarp from roots first)  and  the secret of success is to keep the soil moist until new roots form. This means if it does not rain you need to water. A mulch of wood chips one to two inches deep will help seal in moisture and keep the winter freezing action from uprooting the newly planted shrubs. No need to fertilize until late spring. The first summer you will need to water when top three inches of soil is dry. It takes a few years for a new root system to grow and make these shrubs drought resistant. I recommend you use a soaker hose around the base of the newly moved shrubs so they can have water slowly soaking their roots as soon as the soil dries out. Use a hand trowel to dig into the soil and check for a dark color so that you learn to recognize dry soil over moist soil. The secret is to keep the soil moist but not wet. No need to prune them back but if you need to cut them back for moving don't take off more than one third of the top of the shrubs. I see a healthy new hedge is your future. Keep growing, Marianne Binetti