I don't know what your weather is like but transplanting in really hot weather generally isn't good. Fall or early spring are usually better. However, I have done it successfully.

Wait until fall. With temps forecast for the east coast well into the 90s, the clematis will be under great stress. In your zone, you have the luxury of doing the move in the fall when the plant won't be so stressed. Mid to late September would be a great time to move it IMHO.