Mechanics and Fixing Any Questions Answered

Might be a bit too generic here but I am trying to work out next steps with something.

My son has an old GT with a 1" threaded headset on the original fork, quill stem. The fork has that channel cut into the threads for the old style lock ring headset washers.

I installed a new headset myself (Tange something) when I built up the bike, but now I can no longer tighten it without the top bearing race just sort of slipping / letting loose. It does this before I can tighten it enough to remove all the play. The top lock nut sort of helps, but there still is slop in the headset.

My current theories and solutions are:

1. Headset top bearing race threads are fucked -> replace headset
   
2. Fork threads are fucked -> replace fork
   
3. Not enough fork threads for the top bearing race -> get more threads cut in fork OR replace fork
   
   

I have a new headset and can source a new fork, but I would prefer to keep the original fork if possible. But it may not be.

Which of those three is it most likely? I just want to know where to point the money gun. Ta.