The outside diameter of a 4-40 thread is 0.112. The outside diameter of a 2-56 thread is 0.086. The rod you are using (0.093) is larger than the 2-56 and significantly smaller than the 4-40. The 0.093 just will not allow sufficient material to form a proper thread for the 4-40 size.

For some time now I've been using 7/64" (0.1093) rod for making my own 4-40 rods as required. Granted, this is a difference of just under 0.004 on the diameter, but then cutting the thread is a little easier.

I've never, repeat, never had a 4-40 clevice or nut come loose and I've been using this method for about 10 years.

The threads where the diamater of the unthreaded portion is less than the threaded portion is due to the manufacturing process, which is commonly known to myself as "rolled" threads. This is where the metal is squeezed out of the valley of the threads into the peaks of the threads. The diameter of the unthreade portion will be approximately 0.076 while the diameter of the threaded portion wil be approximately 0.086.

Hope this helps.