Henri Wilson wrote:

The method I use is to reduce the difference between actual
speed and c by a fixed factor per unit distance.

If the initial speed relative to the barycentre of the binary
is say, 1.00015c, then I multiply the 0.00015 by the extinction
rate each light day of travel.

speed relatively to what ? Ether ?

I plainly stated the reference for speed....the binary barycentre..

How does the light know that it should adjust its speed
relative to the barycentre rather than something else?

How does the light determine its speed relative to the
barycentre of the system it has left?

Would light leaving the Moon toward a distant viewer unify
its speed to c relative to the Earth-Moon barycentre or to
the Moon-Sun barycentre?

Leonard