For those whose minhag is to say "half-Hallel"

My B'nei Edot HaMizrach ("Children of the States of the East"?) co-worker tells me that, in her community (Syrian-Egyptian?), there's no such thing as half-Hallel for Rosh Chodesh or the last six days of Pesach/Passover--her community says the complete Hallel whenever Hallel is recited.

But for those of us who differentiate, I recently read somewhere (can't remember where) that we say half-Hallel for all of Pesach after the first (2) day(s) (1 in Israel, 2 in the Galut/Diapora--long story) because of the dignity of the seventh day. There's a midrash that, when the Jews were rescued at the Reed Sea, an event traditionally held to have taken place on the seventh day of Pesach, HaShem rebuked the angels for singing. "How can you sing when My creatures are drowning in the sea?" (This is always the [a?] reason traditionally given for pouring or dipping wine or grape juice out of our cups when we recite the Ten Plagues at the seder.) Therefore, we diminish the number of psalms that we sing for Hallel during Chol HaMoed lest anyone get the false impression that Chol HaMoed (an intermediate festival day when one is permitted to work) is as important as the seventh day, a full chag (when work is not permitted).

Minhag = custom