Actually, yes. Off the top of my head, for a couple reasons.
Gravitational lensing (a general relativistic effect) is observed for distant galaxies. If time travelled slower, there would be aberrations in this effect that aren't observed.
If the redshift didn't correlate to motion, it would mean our galaxy is in a unique gravitational potential well. Gravitational field equations would need a corrective term that is not in any other way corroborated.
We don't know what we don't know, but there are definitely ideas we can rule out.
Gravity is a theory. Although we can fairly accurately predict it's effects, because we don't really know the mechanics of how it works, we do not know what we do not know about gravity.