Perfect mirror is just ideal separator for photons, which should be
allowed for idealized models without energy waste - they don't absorb
heat, only kinetic energy due to momentum conservation.

About argument that there is nothing to use this kinetic energy, there
is no problem to attach a mechanism to mirrors to use it online.
Intuitively 2nd law says that we cannot order energy stored in chaotic
movement, and we've just ordered it into kinetic energy of two large
objects.
About infinite time argument, entropy should change continuously, so
if entropy would be smaller after infinite time, there exists finite
time that it would be already smaller. We alternatively could place
there machinery to use the kinetic energy.
After infinite time everything has T=0 and there is no radiation ...
so entropy is also minimal.

About biology example...
If an enzyme would convert the binding energy to chemical energy of
some molecule (which can be converted into work for example using
myosin), while crystallization we would only increase order - reduce
entropy.
If not - this energy disperse, converting into heat, increasing
entropy.

The temperature is average energy. Most systems has strong property to
equilibrate energy - molecules interacts and energy flows to the one
which has less of it, so usually this energy just diffuse increasing/
decreasing average energy a bit (temperature).
But biology discovered much more stable forms of energy, like stored
in ATP which require a few orders of magnitude more time to share its
energy.

The trick we can use to order energy is to use the energy barrier -
thermal energy behaves statistically, so sometimes will spontaneously
separate the molecules (AB) using energy from heat - reducing
temperature.
But binding them back can be made consciously - store this energy
difference not like usual in kinetic/rotation/vibration which will
diffuse in a moment, but in something more stable like chemical
binding(ATP)/conformation so it could be used later in conscious way.

The choice of direction of the catalyst is determined by
concentrations and energy difference (equilibrium constant).
If (E1-E2) is greater then the energy we've stored (like in ATP or
something less energetic), we will waste (convert into heat) a bit of
it, but favor direction to work as we need.
We don't need to change equilibrium constants - they were chosen while
fixing the enzyme.
I think it should work for some concentrations of all required
molecules. Organism can enforce optimal concentrations.