Unfortunately I don’t think there’s a good solution for this: you have no doubt discovered that you can change the font of e.g. the translation lines for lyrics, or indeed the chorus lyrics, so you could set your Byzantine notation font for that font style, but if you need to change font in order to achieve some specific combinations of symbols, I’m afraid you’re out of luck.
One possibility could be that you find a single font that has implemented all of the Byzantine music notation symbols: as far as I know these symbols are now completely implemented in Unicode (per this note and this table) but I’m not sure whether or not any single font yet implements this block of characters fully. The closest thing I could find with a bit of Googling is this but I’m not sure how complete it is. In theory if you could find a single font that implements the whole of the Unicode range you could use that to reproduce the notation using one line of lyrics and its associated font style.