The difference here is that there is something in the environment that causes the experience of color to appear consistently in many, many human minds. We can measure the waves that could enter the eye and trigger the "color" experience. The same cannot be said of God.

That's not necessarily true. It's possible that we could find the mechanism in the brain which is responsible for spiritual experiences. But that's kind of missing the point. Most human interactions don't drill down this deep. Even rational people have conversation that go, "Did you see that cool fnorble?" "Yeah, wasn't that awesome?" without citing the peer-reviewed academic literature that establishes the objective existence and material properties of fnorbles. Religious people do the same: they say, "Did you feel the presence of the holy spirit?" "Yeah, I did, wasn't that awesome?"

The information on sheet music is compressed, but an individual trained to read it can, with practice, decompress all of it into an experience of the composition.

Sure, but such people are rare. You can probably also train yourself to have spiritual experiences.

a phonograph record cannot be read by (nearly all) humans

Fine, how about this then: display the audio waveform on an oscilloscope. The point is that having music come into your years is a fundamentally different subjective experience than having it come in to your eyes even if the information content is the same in both cases.