Hi, I'm an engineer who's had this same problem, and I think I may have solved it.
I read a post on maybe page 2 or 3 that talked about the blood vessel on top of the foot, which got me thinking.
I was intrigued in my case as to why it might only be happening in one foot. Because it happens when you run, it implied to me that it was some sort of physical deformation happening somewhere in the leg, probably by a generalised swelling.
I looked at the top of my feet the other day and noticed that the blood vessels tracked different paths on the top of my foot. This is what's different between the feet, causing some people to have it in either one or both feet. I cant see anything else that makes the feet different.
My theory is that the problem is a reduced circulation flow caused by shoes simply being too tight.
It makes sense. A congenital defect i thought very unlikely, especially since lots of people seem to have this same problem, and neurologists and other nerve, back, musculoskeletal specialists have all been dumbfounded because they were looking for a "problem" that wasnt there. Dietry or nutritional cuases would imply both feet, and that person who lost weight and had _some_ improvement, implying the extra fat around the foot simply exaccerbated the existing blood flow problem. Some improvements for some people in different temperatures or attempting to looses laces also makes sense; it will work for some people who have a particular shaped foot, vein structure, and run style.
I've started running at the beach with no shoes, and guess what, problem solved.
If you're running in the future and you get stumpy syndrome, TAKE YOUR SHOE COMPELTELY OFF and see what happens and let me know.