אין אומרים הלל בראש השנה ויום הכפורים. הגה: ונוהגין לומר אבינו מלכנו על הסדר, ואם הוא שבת אין אומרים אותו (ר"ן פ"ב דר"ה וריב"ש סימן תקי"ב). ומאריכים בפיוטים ותפלות עד חצות (מהרי"ל).We do not say Hallel on Rosh haShana nor on Yom Kippur. Rema: And we have the custom to say Avinu Malkenu in the order, and if it is Shabbat we do not say it (Ran and Rivash). And we extent with poetry and prayers until midday (Maharil).
Thus, a nice long davening on Rosh haShana, until midday. And perhaps even longer. Magen Avraham writes:
עד חצות - לכל הפחו' (שם) וכ"כ ביש"ש בביצה שבר"ה יוכל להאריך יותר מחצות אם לא כשחל בשב' ונ"ל דוקא בפיוטים ותפלות ולא בניגונים עסי' תקכ"ט ס"א:Thus, at least until chatzot, midday. This would seem to be a lower limit, then. But one is allowed to extend it even further than midday, so long as Rosh haShana does not fall on Shabbat. For it it fell on Shabbat, we would end up fasting past midday, and we should not fast on Shabbat. And, he writes, it appears to him that it is specifically with poetry and prayers, but not with melodies, niggunim.
It seems that the idea is chatzi lachem and chatzi laShem, and people have the inclination to extend it even further in the laShem portion. It would seem that he does not consider the niggunim to really be LaShem to the same extent as poetry and prayer are, and therefore it is not proper to delay the meal given the requirement of chatzi lachem. Thus, chazzanut which overly extends the davening, or, say, an overly long Carlebach davening, might not be good.
Does his exclusion of niggunim only apply to the extension after chatzot, or even up to chatzot as well? I would guess that he only means after chatzot, where there is conflict with chatzi lachem.
I also wonder at the value of extending davening via piyutim nowadays. For some people, it can be inspiring and motivate great feelings, appropriate for Rosh HaShanah. But for many, some piyutim are written in a very literary Hebrew, in which arcane flowery words are used, and even where plain words are used, they refer to things indirectly. Try to say the piyut with havana, that is understanding (never mind kavana), and you cover no ground by the time everyone else has finished zugging the entire piyyut. And just mumbling gobbledygook would seem to me to be no better than extending via niggunim. Perhaps if one decides to prepare beforehand, it is a different matter.