OK, the (totally embarrassing) answer is that I was being far too literal about the example from WebSuperGoo's site. I needed to use the exact font name from my development/production machine.
pdfDoc.Font = pdfDoc.EmbedFont("Times New Roman", LanguageType.Unicode);
Obvious? Yes. But it's one of things that can be overlooked when in a hurry, so I'll post the answer here in case anybody else gets tripped up.
Part of my confusion stemmed from the fact that Russian text added from a URL was just fine in the document, but not the content added as text. I'm guessing that abcPDF sets the font according to the encoding it gets from the web page, but that affects only the content it is pulling in, not the overall PDF.
Anyhow, thanks to gekannt and anybody else who took a look.