You are right, the rikudo give the visual power to one of his son who gave birth to the uhciha and give his physical power who gave birth to the senju. the uzumaki is a clan which came from the senju itself, but the question is why did they change their name to uzumaki. Maybe this clan is the true key for the perfect rinnegan user.
think u need to check on that theory of yours that uzamaki descended from Senju. someone once gave the proof that the SO6P was most probably an Uzumaki, (based on Chakra reserve, lack of use of ninjutsu, sealing techniques, similarity of his seal to naruto's 8 . . .bla bla.. seal and capacity to seal something as big as the juubi into himself.
i think it's the reserve
and seriously i wish Naruto get's the juubi, he's got almost everything the SO6P had, his body, sage mode, power from a couple of bijuus, the SO6P belief system, thanks to JIraiya. + the theory that people acquire the abilities of the bijuu they are jinchuriki to (naruto' s whiskers + how did the SO6P get the rinnegan in the first place, it's so much like the juubi's eyes). so Naruto needs just some few contributions from the 8 tails to activate his own potentials for recreating another juubi.
oh, big question, pls i need to know if Naruto is still with Shisui's eyes