Well after something on the order of 2 years The Guide, and the blogs are working correctly again.
Apparently something in the WordPress core files had corrupted in a way that wasn’t triggering any error messages, just basically making it utterly ignore various aspects of the .htaccess file where the blogs.dir was concerned. It’s embarrassing, really, how easy it was to fix. I mean, it was a sudden spark of inspiration to replace the WP core … and one so bloody obvious that I ought to have tried it a lot earlier.
C’est la vie. It’s working again. Yay!