Yes... I considered this also, in this post. There are some other conservation laws and principles that may apply, and I'm not good enough at quantum physics to identify them.

You can calculate what is permitted by energy budgets as follows. First, split the original photon into the red-shifted photon you want to continue, and another one carrying the difference in energy and moving in exactly the same path. Then take the second photon, and do a Compton interaction with the electron. End result: one redshifted photon on the original trajectory, plus a photon and a recoiling electron.

Electrons don't split up photons in this way, but the energy budget works.

It does not match Lyndon's descriptions, however. There is no absorption; a free electron cannot absorb a photon. There is also no basis for the "calculations" Lyndon gives for the expected redshift. This method works with any redshift you like.

Cheers -- Sylas