After reading the experiences of a number of other folk also having issues with Microsoft Bing (and thereby DuckDuckGo) indexing -- particularly this comment on Hacker News, I've come to the conclusion it was my fault after all.
At some point last year, I redirected my older (mostly unused) domain to this site, but using "cloaking". Meaning the url in the browser stays the same, and it just serves content from the new domain. Clever enough use of the old site I thought -- however, Bing somehow came to the conclusion that the old domain was the canonical one, so it's indexing pages from that domain instead. Basically I'm proxy mirroring my own site and messing up my indexing as a result.
The annoying thing in all this -- there's no indication in Bing Webmaster Tools that "there's an exact duplicate of your content being served from [some other domain]". Which would've been helpful to figure out where I'd gone wrong...