The speed of light in a medium is always some constant specific to that medium times c. If c changes, the constant will not be affected. So I don't see how you

The speed of light in a medium is always some constant specific to that medium times c. If c changes, the constant will not be affected. So I don't see how you could use the speed of light in a medium to deduce anything about c. The same logic applies to gravitational waves. And as long as the speed of gravitational waves is always equal to the speed of light, the relative values of the two will still not change. Say old light speed in glass is k*c1, new speed is k*c2. Old gravity wave speed if n*c1, new is n*c2. How do you you use these numbers to find out if c1 == c2 or not?