I see your point now .
Well we do know that Uzumakis and Senjus are specifically noted as distant relations and that the spiral in Konaha's leaf symbol was put there to honor the close relationship between Senjus and Uzumakis. Again, Both Senju and Uzumaki have Yang energy, both physical and both life force oriented. So honestly it just doesn't feel like Uzumakis and Uchihas have too much going between them.
There could however be a spin, an unexpected spin (as you hinted), in a link between the Uzumaki and the Uchiha, because for all we know, Kishimoto may have had a hidden reason for making the Older Son's eye pattern a spiral.