Thanks V. I'm seeing a similar number of problem search requests (although nowhere near as many real search requests:-), so it is probably the same "SEO practitioners" running the same "scraping footprints" against different search engines around the same time.
I was kind-of hoping that somewhere in this discussion there would be an "And the answer to your problem is...", but I suppose it is a very specific problem which only a search engine would encounter. I think the Cloudflare solution you have is probably the best to block the requests as early as possible. The reverse proxy config[0] I've got seems to be mostly holding out for now though.
[0] https://github.com/searchmysite/searchmysite.net/issues/55