Kinda off-topic: Forenoon! I have wondered forever why the english language doesn't have a word for our german "Vormittag" (or the danish formiddag) and now I have found it! I did a bit of research and apparently people stopped using it around 1800 or something, but it exists and that makes me a very happy person.
You are absolutely right. and this term is in common use, so for anyone wanting the equivalent of formiddag in English in common use today, the term late morning sounds perfectly normal in modern English, not archaic at all, even and is widely known regardless of region, even if most people tend not to worry about specifying:)