Yes. This was, IIRC, an element within de Sitter's modeling in 1917. The view was that the wavelengths would become longer due to time dilation of the atom emitting the photon, thus making it more red than what his observed on Earth.
Others, such as Lanczos, Weyl, Lemaitre, Roberson, and Tolman, also worked within the framework of de Sitter's model. The main competitor was Einstein's own cosmological model.
Einstein knew his model was only favorable in math terms, not in physics terms. His model, as he knew, had no explanation for the redshifts observed by Slipher (1912 and later).
De Sitter's model did offer an explanation for redshift observations, but his model had no matter in the universe. That's a problem.
When Edington showed de Sitter the model from Lemaitre (spacetime expansion of a dynamic universe, not a static one), he immediately recognized its brilliance. By 1931, Einstein quickly corrected his harsh criticism of Lemaitre's model and accepted it.
If you study de Sitter's model, you might find something to help your vision of cosmology.