Hence I am wondering whether May 7/8/9 has anything to do with some changes in Google's treatment of (various?) technical issues of a website.
The only site of mine affected by that one was also the only site affected by Penguin. It recovered a noticable little percentage of its traffic on those days, and has gotten a few more bumps since then. I think it was testing Penguin 2.0 on a limited set of sites.
I'm finding the best way to force traffic is to pay to promote Facebook posts. IMHO, FB is the future for delivering quality / buying traffic.
Glad to hear you're finding something that works! In my niches (informational topics), social media is how more and more people are finding the stuff they used to Google for. While my Google rankings on my top site are still great, it just doesn't deliver like it once did because people are using FB, Pinterest, SU and others instead.