I have no evidence, but I was a punk in San Francisco in the very early 1980s, and I do remember a mosh pit evolution. Initially, the mosh pit was just a place for friendly pogo-ing and shoving. No elbows, and if somebody got knocked over, they got picked up right away. It was all very friendly (except that we used to bang into the hippie fans, which wasn’t very nice of us, but again, we weren’t out to hurt anybody. And we were punk as fuck). Comparing bruises at the end of the night was part of our teen punk bonding ritual.
I seem to remember that modern-day moshing began when the second-wave of L.A. punk bands started coming up. By second-wave I mean the bands that were slightly different in style from bands like X, The Bags, Fear, Catholic Discipline, the Germs (these were more akin to old-school New York and London punk). Bands like Black Flag, TSOL, and especially the Circle Jerks had a very different boy-energy, and I remember moshing changed when they came to SF.
If I had to trace modern-day moshing to a particular band, it would have to be the Circle Jerks. They were from Huntington Beach; we called them, and they called themselves, “HBs”, and there was a particular HB style of dress (which, for a while, was pretty much just a bandanna worn as a headband). There’s an old Circle Jerks line drawing that shows proper moshing form: body bent over, and elbows angled out to strike right and left. This is when we started leaving the clubs with fat lips rather than bruises. Stage diving was a slightly later invention.
Though I am often quick to agree that many of the most enduring forms of pop culture are rooted in New York, I am pretty certain that this one is not, and I would bet what little money I have on it. It makes sense to me, though, that the first New York moshing incident occurred at a Black Flag concert, and this seems to support the argument that moshing as we know it started in L.A.
A good source may or may not be the crowd scenes in Penelope Spheeris’s documentary, The Decline of Western Civilization–this might still be too early in the evolution, though. The best evidence, though, would come either from someone in the Circle Jerks, or Black Flag, or someone who was in L.A. at the time.
Hope this helps. I’ll look forward to hearing what other people remember.