Short-changing the last day of Pesach with only a partial Hallel

There are two reasons given why we only say a partial Hallel on the last day of Pesach. The most prosaic of which is the fact that the sacrifices were the same during the intermediate and last days of Pesach, so no complete Hallel is required since they are all subsumed under the same rubric (B.Talmud Erchin 10b)

The more evocative reason is that when Israel made it across the Red Sea, the angels wished to sing praises, when God chastises them by saying, "The work of my hands is drowning in the sea, and you wish to sing?" This is the reason that people know, primarily because it is the only reason quoted in the later codes. Never mind that we sang and danced when we crossed the sea.

The first time this reason appears is in the 13th century work Shiblei HaLeket of Rabbi Tzidkiyahu Ben Avraham HaRofeh when he quotes from the lost Midrash Harneinu:

Shmuel Bar Abba said: "At the fall of your enemies, do not be joyful." Because the Egyptians were drowned [we do not say a complete Hallel]. In later Halachic works the Talmud in Sanhedrin is quoted to illustrate this point, "The work of my hands is drowning in the sea, and you wish to sing?" Even more interesting is that the more prosaic reason is not mentioned at all having been eclipsed and embellished by God's empathy for the Egyptian enemy. In the collective Jewish memory, this is the reason most people seem to know, the source of which is a lost Midrash, which is buried in a section of the Shiblei Haleket, the subject of which is Rosh Chodesh (The New Moon). Dredged from the innards of a 13th Century halachic anthology, comes a truism in Jewish consciousness.

Blessed is the people who wish to believe in God's empathy, and in so doing, believe in their own.
Chag Sameyach!