I been surfing around industrial thread standard resources. This is one of the industrial standards in use in the world currently, and this is what I think the standard bicycle spoke thread is:

2-56: 0.0860 or 43/500 in diameter; 56 threads per inch

.0860" happens to be extremely close to 2.2mm, which is why Park Tool also appears to be correct.

Also by direct measurement spoke thread diameter under my mic is .086". (It was counting tiny threads which was difficult without the right tool.)

Thanks, MudPie, for the rad Park Tool link, I'll be revisiting that page for other stuff too!

So to conclude (note to self!) -- if I'm going shopping for matching nuts, it's 2-56 standard nuts which I will need to find.