Hey Eric,
I don't think it's disputable that the ANE had an influence on Israel and I don't think it's disputable that Egypt had an influence on Israel. Actually, we don't have to look any further than the texts within our canon to see this fact. However, I think that the story is different than the stories in the ANE or in Egypt in many ways.
Take for example Abram who was called out from the heart of ANE culture and YHVH tells him to sacrifice his only son Isaac. Abram doesn't bat an eye partially I believe because in the ANE, human sacrifice was not uncommon and I'm sure you already know this, so, from Abram's perspective why would YHVH expect any less than the gods of his former land?
The difference I believe, is that YHVH does not allow the sacrifice which was revolutionary in Abraham's day and the culture that surrounded him... and there are many other distinctions like this that buck the norm of the ANE.
So I think anyway, that yes, there are a lot of common threads between the stories of the Bible and the ANE, but the way they are handled (e.g. creation {1 - 2 Genesis}) were revolutionary in their day.