The short answer I don't know, I didn't have teachers and my friends cannot understand this type of discussion, so their are gaps.
I think that as long as the particle is not moving and its time matches the space it is in, the light it emits (when it enters our slower time) should be the same as on Earth. I argue this from conservation of energy.
Imagine that you had a clock next to this atom. Time moves faster for this clock than for us, correct? So to us, the clock would appear to be moving too fast, though not for the atom.
But radiation from the atom IS a clock. Its frequency, as emitted by the atom, has a specific relationship to the speed of the clock sitting next to it. So if the clock appears to us to be ticking too fast, then the radiation will also be shifted to higher frequency, because it's a clock too. So the conclusion that the frequency will be shifted is unavoidable. You CANNOT have time move faster and not shift the frequency as well.
Now, that doesn't mean we get to throw energy conservation out the window. We must address it. But energy conservation doesn't mean that no shift occurs. Rather, energy conservation means that any shift must go hand-in-hand with a change in potential, and this potential must be energy and mass based (ie, gravity). And that's exactly what happens with general relativity.
So we've actually discovered that your theory has an internal contradiction: your time rate theory requires that the frequency shift depends on the strength of the gravitational field, which is the
gradient of the gravitational potential. But energy conservation requires that the frequency shift depends on the gravitational potential itself.
General relativity has no such internal contradictions. It has been experimentally tested in many ways. Gravity-dependent time dilation has been measured, and it agrees with the predictions of general relativity. So why do you think we need to replace general relativity with something else? But whatever your dissatisfaction with GR might be, and even if it's wrong, your alternative clearly will not work. It is internally inconsistent, and it doesn't match observations.