I somehow found Mojeek and settled on it. I had never heard of them. Unlike Kagi, their business model is ads (so they hold no particular moral high ground). But they have a cheap, working paid API.
What I was astonished by is the quality of the results. For my uses, it's undistinguishable from Google. The conventional wisdom is that web search is a Google-sized problem. How did those obscure Brits pull it off?