Speed of gravitational waves vs speed of light

Not really. The "speed of light" has very little to do with light; it is built into the actual geometry of spacetime independent of what matter fills it.

In particular, $\epsilon_0$ and $\mu_0$ don't tell us anything physical about the vacuum; looking at the (simplified) expressions $$E = \frac{1}{4\pi \epsilon_0} \frac{q}{r^2}, \quad B = \frac{\mu_0}{4\pi} \frac{I \times \hat{r}}{r^2}$$ we see that $\epsilon_0$ and $\mu_0$ just define the units of the electric and magnetic fields. We can (and often do) change their definitions; for example, in Gaussian units, we set $1/4\pi \epsilon_0 \to 1$.

Nonsense. Maxwell derived his electromagnetic equations, with epsilon zero and mu zero, and those quantities were known. The fact that his equations led to the speed of electromagnetic waves to be, in terms of epsilon and mu zeros, equal to the approximately then known speed of light is a big part of what led Maxwell to conclude that light is electromagnetic.

No coincidence, light is electromagnetic and those entities define the speed of propagation of electromagnetic waves.

See Jackson or any other good electromagnetism textbook for the derivations.

Btw, it's not about units. E and B are simply used to define forces, and the values of those were known, so epsilon zero and mu zero were also approximately known.

Finally, it's gravitational wave speed also because Einstein got GR (general relativity) through a (mind blowing) generalization of special relativity to an arbitrary frame of reference, with gravitation equivalent to acceleration (equivalence principle). SR (special relativity) included c, the speed of light, as the maximum speed possible, achieved by zero mass particles. GR had to reduce to SR in a local inertial frame, so it also had to include the same c. GR waves reduce to a Lorentzian wave equation with c, in the weak field limit. Also in a local inertial frame.

Theoretically it all adds up, there's isn't any other way if GR is true. The way it might not be totally true, with respect to gravitational waves going at a speed different (and necessarily slower than ) c is if the graviton (the presumed quanta carrying the gravitational radiation or force) is a non-zero mass particle. Based on measurements of gravitational effects in the solar system it is known the mass of the presumed graviton is zero to about 1 part in (and here I am not sure I have the correct number, but it is to great accuracy) maybe about 10 to the fifteen or eighteen. The eLISA satellites to be launched in a few (2-3?, see Wikipedia on it) years will measure it even better by seeing if there is any delays between different frequencies of the gravitational waves they will see - it'll have orders of magnitude more accuracy, it's interferometer baselegs are 1 million Kms compared to the 5 Kms of LiGO which recently detected gravitational waves.

A better way to think of it is "speed of causality". That's the fastest any cause-and-effect will spread over space.

With nothing to cause it to go slower, changes to electric and magnetic fields will occur at that speed. No coincidence that changes to spacetime (causing gravity) propigate at the same speed.

You really need to show how Minkowski spacetime results in such a speed limit as a basic principle. It's not a speed limit in the usual sense; it's a deep principle of what speed is.