Yes to all of the above. You need a thin wall 9/16" socket (made by me by judicious use of a drill drive for 3/8" sockets and a bench grinder). Yes, the single point turning followed by a die was what I was thinking - I am pretty sure I have the right change wheels for my lathe. I think the cap screws would be better than the hexes.
I'll see if I have a cap screw at least suitable for trying this before going and buying a set to work on. Do you think they are likely to be soft enough to machine?

