Hi Randomlydunn, welcome to SDC!
As Ramparts said so succinctly, the influence of mass on time and redshift is not a significant factor.
The influence you refer to is known as gravitational redshift, and is essentially due to the difference in the gravity where the light was emitted, when compared to the gravity where the light is detected. Unless there is a very large difference, gravitational redshift is a very slight effect and is hard to detect at all.
To put this into context, apart from our own Sun (where the difference in the gravity of the Sun to the gravity of the Earth allows us to measure a very slight gravitational redshift), we can only expect to find (relatively) easily measurable gravitational redshifts for objects like neutron stars or black holes. We would see the light from a neutron star as being gravitationally redshifted, whereas someone near the neutron star would see the light from the sun being gravitationally blueshifted.
One way to think of it is that light is redshifted or stretched as it climbs up a gravity gradient, and is blueshifted or compressed as it slides down! If the light has done more climbing than sliding, the observer sees a redshift, and vice versa.
The same is true at the scale of galaxies - unless there is a large difference in the mass of two galaxies, the effect is hardly measurable. And it is only the difference between the original emitter and the observer that causes any apparent change in the light, it doesn't matter whether the light passes many very dense objects on its journey, as the light is always blueshifted "on the way down" by the same amount that it is redshifted "on the way up"!
But with the expansion of the universe, the light is actually stretched to many times its original wavelength! We see galaxies that look to be a similar size to our own, but highly redshifted by the expansion of the universe. We see the Cosmic Background Radiation - originally emitted as visible light, but now stretched into microwaves by the expansion over 13.7 billion years.
Now, with both gravitational and cosmological redshift, you get a form of time-dilation (which once again for gravitational redshift is negligible compared to cosmological redshift), but that's another story, and the important thing to note is that all this has already been taken into account in the current cosmological model.
Nice idea though!
(edited to correct a few typos or grammatical errors)
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