You wrote: "Fascinating paper! It looks very much like you've got the other side of the story I have presented in the context of extended GR."
Yes, it does seem like our two respective approaches are flip sides of the same coin. I have arrived at the parallelized spheres via an analysis of EPR and Bell, whereas you have arrived at them (it seems) more from the particle physics side. But the conclusion seems inevitable:
"Physical causation will only be consistent and complete if it realises all the manifolds S0, S1, S3 and S7."
By the way, we are not the only ones who have recognized the significance of these manifolds for fundamental physics. Geoffrey Dixon, Rick Lockyer, and Michael Atiyah (to name just a few) also seem to share our conviction.
I also agree with your proposed meta-principle for my work, although I would use a slightly different language:
"Locally causal representation of reality (in the senses of EPR and Bell) can only be consistent and complete (in the sense of Einstein and EPR) if it is based on a parallelized 7-sphere, S^7, which contains S^3, S^1, and S^0 as nested submanifolds, in the manner of Hopf."
This is more mouthful than what you have suggested, but it describes what I am proposing more accurately.
I am not sure how to answer your other question:
"However, the consequence of this restriction is that the symmetry breaking required to give topological monopoles must be of the form:
S7 = SU(4)/SU(3) -> (Spin(3) * SU(2) * U(1))/Z3
Which would imply that the local colour group HAS to be SO(3) and not SU(3). Once the significance of the manifolds S0, S1, S3 and S7 is recognised there doesn't seem to be a way of avoiding this conclusion. Does this seem correct to you?"
I am not sure about this, mainly because I am not a particle physicist. What I am 100% sure about is the significance of the manifolds S^0, S^1, S^3, and S^7. If this implies what you think it implies, then I would put my last penny on it.