Without a doubt, I would certainly threadmill those threads. As long as the threads are still 60 degrees, you could use an off the shelf threadmill for 7/16-20 threads to acccomplish this. I just checked the price at $115.
Threadmilling is also a much more secure process with larger threads, and the threads turn out a lot prettier.
I would imagine that inspecting the major diameter is going to be the expensive part, if you have to buy a gauge...I hope you have a part with the external threads!