Thank's for the details.
Sorry, but I can't help you. My lathe doesn't have enough spindle bore to chuck up a complete M4 upper.
Also I don't have a threading die in that size (32x1,5).
If you find someone with a suitable thread-cutting die, please don't forget to undercut the mentioned part (approx 0,3 mm down to 31,7 mm), otherwise you will get problems to cut the thread.
Kindest regards.
Jati