Since a new version of the free-as-in-fork LibreOffice package was just released, I thought I’d take a look and see if it’s gotten any easier to import formatted text.
The answer: “kinda”.
Good: It imports simple HTML and CSS.
Bad: …into a special “HTML” document type that must be exported to disk in ODT format, and then reopened. Otherwise, all formatting not available for web use will either disappear from all menus and dialog boxes, silently fail, or be deleted when you save (generally the result of pasting from another document).
[note that the Mac version crashed half a dozen times as I was exploring these behaviors, but it usually managed to open the documents on the second try]
Sadly, furigana are not considered compatible with HTML, so they’re stripped on import, making it rather a moot point that you can’t edit them in HTML mode. The only way to import text marked up with furigana is to generate a real XML-formatted, Zip-archived ODT file.