I would like to just add an update. Last night, I ran across a couple old boxes of SA matches in the back of a cupboard. I compared them with the "new and improved" Diamond SA matches I picked up when I started this thread. Indeed, there is significantly more of the white phosphor material on the new matches.

I scraped the white material off an equal number of the old and new matches, and using my expensive laboratory scales, carefully weighed both and compared all the samples. The white material on the new matches weighed significantly more (.05 significance level on a standard statistical t test) on the "new and improved" matches than the old and "unimproved" matches.

NOT! OK, I just eyeballed it with without my reading glasses on. But truly, those old matches wouldn't light for shift, while the ones with the more white phosphor will, as I've said, easily light on any roughish piece of paper (e.g. standard brown paper bag).