"If those frames were truly independent, then one could be passing through another, each with their own C. It is because these frames add up to that larger set that it works."
No, this a common mistake, John -- and it leads to a lot more of the bizarre contradictory claims in this forum, than yours.
Because all physics is local and there is no privileged frame, the theory is observer dependent -- meaning that there is no boundary between the observer and observed at any scale. In quantum mechanics, it is believed that a phenomenon called quantum entanglement explains what would be a contradiction if not for the mathematical artifact of superposition and the physical assumption of nonlocality.
In principle, this is exactly what you claim above: the assumed independent frames are ghostly superpositions, and the sum of that "larger set" is the set of nonlocal events.
For those who believe in quantum mysticism, this explanation is good enough. The model is entirely incompatible with special relativity, however -- because it assumes, as you do, that boundaries, expressed as particle path histories, are independent and bounded and tractable to linear summation.
Probably the hardest thing to understand about special relativity is that the lack of privileged observer frame renders all observed results local, because time and space are continuous. Time drops out of quantum mechanical equations, however, which is the very same thing that allows you to claim "independent frames." There are no independent frames -- only independent observers.
When locality is everywhere preserved, the only entanglement is classical, i.e., orientation entanglement of observer to observer, and measurement results in every inertial frame are valid, leaving no physical boundary between quantum and classical spacetime domains.
Best,
Tom