you picked one set of numbers, calculated something, then didn't like it, changed from 1 to 10 megajoules per square metre, that's not how you do it if you are thinking straight.
Regarding 'my estimate', once again: 500 megatons is total testing, 10 ... 100x the figure you picked, total 5000 .. 50 000 megaton , the 1 megaton of tnt is 4E15 j , times 5E3 = 2E19 , times 5E4 , 2E20 .
Top it off by the smoke not going into stratosphere from a bush fire because there's too little intensity, it doesn't even burn all at once, so there's nothing whatsoever even comparable about those numbers in the first place?
What part do you not understand about "you have been conclusively demonstrated that you are not thinking straight about existential risks" ? People have two reactions to existential risks: be sure that it exists, be sure that it does not, proceed to not thinking straight one way or another. Sagan demonstrably screwed up with oil well fires, yes. You are demonstrably screwing up right now. Nobody's safe from it. I'm only reasonably sure i'm not screwing up because i haven't been called on bad math, and haven't got very strong belief about nuke winter.
Americans have 10000 atomic weapons currently. Russians also. Others are negligible in this sense.
Say that the average bomb has 1 MT. This means 8*10^19 J of energy. What is a big overestimation, but for the sake of the discussion, would you accept this number first?
Just a reminder that some of the old threats are still around (and hence that AI is not only something that can go hideously badly, but also some thing that could help us with the other existential risks as well):
http://blog.practicalethics.ox.ac.uk/2012/03/old-threats-never-die-they-fade-away-from-our-minds-nuclear-winter/
EDIT: as should have been made clear in that post (but wasn't!), the existential risks doesn't come from the full fledged nuclear winter directly, but from the collapse of human society and fragmentation of the species into small, vulnerable subgroups, with no guarantee that they'd survive or ever climb back to a technological society.