There is a nontrivial relation between the electric charge and the strong business, namely that there are instantons which will cause proton decay. So it is not completely true that there are no relations--- the requirement of anomaly cancellation requires that the proton decay process conserve charge, and so relates the total charge on the proton to the total charge on the electron.
The U(1) numbers are completely crazy. The only sensible explanation is that they come from an SU(5) GUT (or SO(10) or E6 or some higher version of the SU(5) idea). The reduction of charges from SU(5) is explained in this answer:
Is there a concise-but-thorough statement of the Standard Model?
This gives the 1,2,3,6 ratios of the hypercharge assignments in nature, and completely explains the crazy quark charges. It is also an automatic way of ensuring anomaly cancellation. This, and approximate coupling constant unification, are the two strongest bits of evidence for a GUT at a scale of $10^16$ GeV or thereabouts.