There may be a form of information transfer that’s much faster than light, on the longitudinal axis of gravity.
The same possibility holds true for gravitational waves, since they are unimpeded by matter as well. They even have the advantage of propagating at the speed of light, unlike neutrinos.
> For example, it can take thousands of years for the light produced by fusion in the Sun to reach the surface of the photosphere
This is not due to free travel of light through a transparent medium with a high index of refraction or due to gravity. Through a large part of the sun energy is transported by convection and even in the radiative zone photons get frequently absorbed and remitted, the mean free path is below 1cm.
‘Slowing’ down light by putting it in a reflective cylinder, water or fiber optic cable doesn’t change the nature of the universe or help achieve faster than light information exchange - it just means some photons are experiencing a traffic jam.