Well, the advanced DIY efforts yielded nothing, so a professional plumber came in this morning. He had a power snake, which impressed HRH a lot.

The crap with which they’d plugged the drain broke the snake.

Eventually, with a high-powered water jet machine that had it own major compressor, the plumber punched through the crap. He flushed the pipe clean for about half an hour. We now have a kitchen sink again.