The problem is, this is something we observe every day - and those observations prove you wrong. Indeed, that was the whole point of the Pound-Rebka experiment - but it's also observed in cosmology all the time.
And the reasons for that are quite obvious and have been nicely explained by Zig. If time is moving faster for the atom, then it emits light of a higher frequency by definition of "time moving faster for the atom".
If it is moving
in any time frame it will change the frequency. If it is moving at relativistic speeds, time will add with the Doppler shift.
If it is fixed, (not moving), within any time frame, it does not change.
An atom in a 10X time space will emit a photon with 10X the frequency.
The photons path to an observer will shift the photon back down to our 1X time, it will look normal.
The difficulty of determining an absolute framework is actually worse.
The difficulty from both standard relativity (and I hope you mind, if I call it Extended Relativity) is determining your absolute velocity, within the space you occupy.
I don't believe that this is possible, because the failure of the Ether experiments. Velocity does not appear to be an absolute measurement. We can measure our velocity only relative to other frames.
The velocities in those frames are relative to the time flow, in that frame (Time Space).
Their velocity is relative to their own time frame (Time Space), then it is relative to our velocity in our (Time Space).
If anything, the absolute time frame problem is much worse.