Cosmological redshift - How do we know it's not caused by the observer's time dilation? Instead of cosmological redshift being caused by the metric expansion of space, why couldn't cosmological redshift be caused by our perspective moving faster in time?  Said another way, if the observer moved through time faster than the emission source, couldn't this time dilation be an explanation of cosmological redshift?  Instead of the metric expansion of space, why not "cosmic time dilation"?  

As far as I know, there is no physical mechanism in physics to explain how the metric expansion can cause red shift.  It appears that we assume metric expansion can cause red shift with no underlying physics or testing.   

Alternatively, red shift caused by time dilation is well tested, proven, and understood.  It is something we can play with here on Earth.  

Wouldn't assuming cosmological redshift is caused by the observer moving faster in time than the emission source in the past makes more sense than the metric expansion of space causing cosmological redshift?

Of course when measuring redshift from distant sources, the Doppler and gravitational effects must be accounted for.  That's not what I'm asking about.  

Edit:  I probably need some math help, or a pointer to a better example to play with.  

With a Hubble Constant of 71.9, a lightyear expands about $7.3483\times10^{-11}\ \%$ per year.  The Pinwheel Galaxy is 20.87 million light years light years away.  If I continuously redshift the Pinwheel Galaxy by the expansion of space, I get a redshift of .00153 using this equation:  

$z = 1 - e^{(7.3483\times10^{-11})(2.087\times10^{7})}\ $

The pinwheel galaxy has a measured Redshift of .000804.  

Is there an equation that gives a better result without magic values for $z$ or a real world example with known values that works?
The reason we think that the cosmological redshift is caused by the metric expansion of space is 1) that there is a well-known, physical mechanism that can cause this effect, and 2) that this mechanism is a prediction of a well-established and thoroughly tested theory, namely the theory of general relativity.

The physical mechanism in question can be realized by considering the propagation of a light ray traveling along a null geodesic in the Friedmann-Robertson-Walker metric describing the expanding space (see e.g. Watson 2000 for a derivation). It is a mathematical result, but it is founded on physics, and verified through experimentation.

On the other hand, there is no known mechanism that would cause time to speed up as the Universe evolves. Moreover, even if there were, this would only make photons arrive less often in our reference frame (compared to photons arriving from a local object), but it wouldn't make the individual photons have less energy (unless they somehow kept oscillating at their original frequency, even if entering a reference frame where time goes faster).

But in a sense you're right that our time goes faster than the time of distant objects: In our reference frame, their time is slower by a factor $(1+z)$, where $z$ is the observed redshift. For instance, the brightness of a supernova observed at $z=1$ declines twice as slow as a "local", $z=0$ supernova. This effect is well-known and "in addition" to the redshift, in the sense that the flux received on Earth is diluted by a $(1=z)$ factor from the redshifting and by a $(1=z)$ factor due photons arriving at a slower rate.