The Egyptian and Biblical timelines can't really be fit, due to the lack of information. If we accept the generaly accepted theory that Moses lived during the reign of Ramesses II, then Tut's contemporaries could have been Joseph and his brothers (Ruben, Levi, Simeon, etc.) or his descendants. (If the Biblical story is true, it can also explain the origin of Akhenaten's monotheism: Joseph, the monotheist Jew arriving in Egypt - becoming friend of Pharaoh, possibly Amenhotep III - having a deep impact on the young prince Amenhotep who later becomes Akhenaten...)
The Bible also says that after many generations the ruler was a new Pharaoh, "who didn't know Joseph" so the Jews had to escape. This is pretty much resembling the story of Horemheb who founded a new dynasty and was opposed to everything that belonged to the former dynasty (okay, except for Mutnodjmet.