I think what I find confusing is that I thought outside observers would never see the infalling observer reach or cross the EH due to time dilation.
I’ve read that an observer falling into a black hole would notice extreme time compression in the external universe (observing millions or billions of years pass in the external reference frame), and conversely external observers would notice extreme time dilation of people and redshifting of photons falling into the black hole. Infalling particles from their external perspective appear frozen and smeared into a blur outside the EH, fading away but never optically appearing to “enter” into the BH, even though physically these particles indeed have/will.
So I think I had it backwards, the external observers would see infalling objects redshift, and those falling in would see the universe blueshift (I guess getting fried by high energy photons before being torn up by tidal forces).