Lets see if I understand this. 1/2 inch diameter = 4/8, then take out
3/8, leaving 1/8 divided by 2 leaves 1/16 inch for set screw thread.
Do you care if the end of the set screw extends out from the surface?
Won't catch on anything?

Seems like not many threads for a set screw.

I re-measured and the interior hole is 1/4" ... not 3/8" . Good catch!