The first thing I noticed when reading this translation was that instead of being called "Set" this character was called "Typhoon." I think this is probably because Set is the god of storms and disorder among other things. This makes it likely that the Greeks would have called him by their word for storms and disorder, and then when translating to English this would have been translated as "Typhoon."
I found no mention of dancing throughout the myth on this site. This is a vast difference from how Reed focuses on Osiris's dancing as his most important characteristic in Mumbo Jumbo. It is therefore apparent that Reed is not using this story as it is generally accepted in ancient history. There is also no mention of a text being recorded about these dances that were not in this version of the myth. However, the Book of Thoth, as Reed calls the text of Jes Grew, is mentioned elsewhere in Egyptian history. Instead of containing dance moves it is said to have 2 spells, one allowing the user to talk with animals and the other enabling the user to see the gods.
Another discrepancy between Reed's version and the source I found is how Set/Typhoon kills Osiris. In Mumbo Jumbo Set brings Osiris back to Egypt by spreading rumors and then challenging Osiris to "Preform the feat of the Germ" (165) and be planted in the Nile to spring forth again. Osiris eventually agrees to this challenge and is sealed inside a coffer using nails and molten lead. He does fine, laying under the waters in a "death-like slumber," but when Set and his followers open the coffer, they mutilate him to make it look like he was torn apart by fishes.
According to the source I found, Osiris returns from his travels without any influence from Typhoon, who pretends to be a loyal servant. However, Set has formed a group of 72 conspirators and laid his plans, in secret obtaining exact measurements of Osiris's body which he uses to construct a perfectly fitting, decorated chest. He then brings this chest to a feast and says that whoever fits into the chest most exactly will win it. When Osiris tries it he fits perfectly of course, but Typhoon and his followers immediately close the chest and seal it with nails and molten lead. They then put this chest into the nile and it is carried out to the sea. Later, Osiris's dead body is found and Typhoon cuts it into 14 pieces and scatters them across Egypt.
I think that by comparing these two stories it is clear that Reed had read the version found in this source or a similar one. He uses the same idea of a chest sealed by nails and molten lead which is thrown into the nile. The question is then why did Reed change the details of this story. It is clear why he made the changes he did regarding the dancing Osiris and the Book of Thoth, but why did he modify the way Osiris is murdered?