@bangstrom
Your are confusing 2 things: dimensions and units. The dimension of speed is distance over time, independent of which units you use: miles/hour, meters/second, feet/minute. For every different unit the value of c is different. If the units are fixed independently (with feet or arms of kings e.g.), the value of c is a measurement in terms of these units.
But now physics has turned the definitions around, because of the rock solid empirical evidence that the speed of light is invariant. So now it is possible for every sufficient equipped laboratory to 'create their own meter or second' which will be exactly the same as in any other laboratory. Similar for u0 and e0. Because of the relation between these and the speed of light, and light now has an exactly defined speed, one can define the value of one in terms of the other.
Further, let's go with your idea of a 'dimensional ratio': speed is a perfect example of such a ratio. It is the ratio of distance to time. So take my favourite definition of c: it is the conversion factor between space and time if one wants to unite space and time into spacetime, so if you want, a ratio (like an exchange rate of currencies). Now physics shows that this c is the limiting speed of causality: massive particles can never reach this speed, but can come as close to it as you want, given enough energy. Phenomena like light, gravity (and as I recently realised, the gluon field (gluons are massless too)), have exactly this speed. So we get that this ratio dictates the exact maximum speed of causality:
a causal relationship involving massive objects can never be faster that c
a causal relationship involving massless particles is exactly as fast as c
a causal relationship involving 'just information' is dependent of the previous two. Information needs a medium, be it massive or massless particles. So 'information' is also bound to the limiting c.
So this means that in entanglement, no information can travel fast enough to inform the other particle what e.g. its spin must be. So there is no information exchange, no causal relationship between the two particles, no action. And this is also not what follows from Bell's theorem. Two alternative formulations of what follows from Bell's theorem:
If you measure the spin from 'your particle', you immediately know what the spin (measured in the same direction) is from its entangled partner. (Similar as the example of a left and right hand glove. Nothing travels from London to Sydney to 'make' the other glove a right hand glove.) But is only your knowledge of a remote event, and that has no limiting speed. Nothing in the measurement of the other particle shows that the first was measured. Only by comparing the measurements one notices the correlation.
If you want to model entanglement with classical means, you would need faster than light communication. However, the quantum mechanical description does not need any communication.
As said before, the reason is that the measurements of the spin of the two entangled particles are correlated: the interesting thing is that they are stronger correlated than can be classically explained.
Given our daily classical conceptions, quantum entanglement is an astonishing phenomenon. But it follows directly from quantum mechanics itself, without needing information exchange.
Do you see now that this problem does not exist?
It is not an action, as explained above.
It is both, as explained above.
It is correlation, as explained above.