Rather than make a cut, add a section in and move original thread up, giving two joins, I'd simply replace the top section and cut a new fresh thread.
That way the internal reinforcing insert can be smaller. Good idea as you need to make sure that it doesn't interfere with the stem fit, but it also can't be so long that the butt on the steerer gets in the way.
I can do it for you, and have steerer tubing, the die and handle to cut the thread, too. PM if interedted.
All the best,