I think the problem you try to solve goes away when it becomes clear that the Bible is not the Qu'ran. That book is supposed to have been written directly by God. But the Scriptures do not claim that status for themselves. They were written by humans "inspired by God"—an ambiguity that I think Islam tries to avoid.

"Forgery" is much too strong a word to describe this process. "Accretion" is more accurate and not pejorative.