I'll try again: General relativity comes with a generic mechanism to compute frequency shifts. We don't need to try to figure out whether or not the effect is

I'll try again: General relativity comes with a generic mechanism to compute frequency shifts. We don't need to try to figure out whether or not the effect is due to time dilation or spatial expansion, we can just do the math. But if we're lucky, we can find a way to split up space and time that allow for such intuitive interpretations. However, that's window dressing, so to speak. All this assumes that the spacetime in question is already known, but that's how it actually happened historically: Friedmann and Lemaitre derived their solutions by imposing certain symmetries on the problem. From that, you can derive observations like redshift (Lemaitre had already done so by 1927, ie two years before Hubble published his paper), which you then compare to observation in order to fix the parameters of your model, or scrap it if it cannot accomodate observation. As far as I'm aware, at no point in time did a physicist sit down and think "I wonder, what's the best way to incorporate redshift into my model, time dilation or spatial expansion?".