I'd like to research this topic further, but I think there will be a lot of information to wade through. Primarily, I would be interested to know the reliability of these other source materials, paticularly with regard to their dating and transmission.
One assumption that could be made is that these events and circumstances didn't really happen, and that NT writers or editors copied these ideas into the Gospels to make Jesus someone he really wasn't. For a "faith-based" explanation, I'd like to propose that these concepts that had applied to the other "gods" were a foreshadowing, or precursor to Jesus, meaning that God took these concepts that had been previously applied to man-gods that people were aware of, and had Jesus's life conform to these kinds of circumstances, as if to say "OK, this is what you expect of man-gods. Well, Jesus conforms to this." In other words, these ideas weren't simply appropriated by the NT writers for their accounts of the life of Jesus, the events actually did happen as they are recorded in the Gospels?that God simply arranged events of Jesus's life to fit the concepts about other god-men to prove a point to people of pagan cultures. (It might even be possible to say these could be distorted prophecies, where people caught a brief glimpse of the future messiah of the world, but couldn't see it accurately and ascribed it to someone else.) You can speculate how many of these concepts the NT writers were aware of when they wrote their manuscripts, but that is why God moved the writers to include them.
I realize that some people may have a problem with the idea of God using pagan teachings in His favor. Paul didn't seem to have a problem with it. When he was in Athens (Acts 17), instead of rebuking the Athenians for worshipping false gods, he tells them he has noted how religious they are, and that they believe there is an unknown god. He then proceeds to use this belief to introduce his God, stating a spiritual truth in the process that actually came from a pagan philosopher-poet.