The Big Picture

As you deduced, Khufu was a type of Jacob. In every dynasty there seems to be someone who assumed the role of Jacob, so there are a number of distinct "incarnations" of this type. For example Senusret II of the Middle Kingdom and Amenhotep II of the New Kingdom. The Hyksos Jacob was called Yakhub-Hor. There are others. And for every Jacob we can expect a Joseph. All the roles were recycled.

The main Biblical Jacob was Amenhotep II and the main Joseph was his son Yuya. The main Moses was Akhenaten. However, there are traces of earlier Jacob's, Joseph's, and Moses's in the accounts of these Patriarchs.