Good Shaila.
I looked at a few seforim, nothing much.
Two Ideas though of mine (not mentioned previously) both pro and con:
For being able to daven Musaf: There is a shaila by sefiras haomer and blowing shofar in the same scenario of early shabbos (after maariv). The Taz says no, but I believe the Halacha is (I think R’ Moshe agrees with this opinion) you can blow shofar or count sefira or read megilla…with brachas and details I don’t know. So to, it would seem, it still is Friday and R”H but just tosefes shabbos on top of that. By mincha it is different because you davened maariv, musaf though is connected to the day, which still is lasting til shkiyah.
Against: there is an halacha I don’t understand but seems to be the main opinion. When R”H falls on motzei shabbos, one should be particular to stop eating before shkiyah because if it not it would be a stira in bentsching. I don’t get that because it is still Shabbos because of tosefes shabbos and it is now Rosh Chodesh. I don’t get why that is a contradiction. But most seem to disagree though some say both retzeh and yaaleh v’yavo. Not sure if this is same by our case, but it could be similar regading being contradictory.
DQB