I'm not an astronomer, but my intuition is this: When the source of the light is moving towards the observer, each successive photon emission happens from a position closer to the observer than the previous photon. Hence, from the observer's perspective, the time between photons is reduced, meaning more photons are observed in a given time, and the brightness is increased. When we observe a galaxy that is rotating opposite to us, not only is the source of the light moving closer to us, but we are also moving closer to it.

From the perspective of us looking directly down on a parallel “plate” of a galaxy (with the other galaxy viewing us in the same way), relative differences in speed for the situation of same direction of rotation will be much smaller than for opposite directions.

But between any point in one galaxy to another, just as much matter will be moving closer as moving away. Regardless of same or opposite rotations.

But perhaps greater red shift and greater blue shift (as apposed to lesser of both) as a practical matter of telescopes vs. their cross spectrum sensitivities, means more light detected.

I would assume that they're talking about redshift.

Yes, but one half of a galaxy would get redshifted, and the other blueshifted, no matter which direction it spins in. So why would that change its overall brightness?

(Though one of the papers notes that the tiny change in brightness this causes isn't enough to explain the large difference in spin directions)

The close and far sides get shifted too, and those have different brightness.

No, 'like_any_other has it right: any physical system is 1-to-1 isomorphic with its mirror image, which is spinning the opposite direction.

Whatever asymmetry you're visualizing for one galaxy, its mirror-image galaxy is equally physical, and possesses the same asymmetry.