So, electromagnetic waves travel below $c$ if they're not traveling through the vacuum.
Do we know (or have a theory of) whether gravitational waves always travel at exactly $c$ or is there something that could slow them down?
So, electromagnetic waves travel below $c$ if they're not traveling through the vacuum.
Do we know (or have a theory of) whether gravitational waves always travel at exactly $c$ or is there something that could slow them down?
Yes they always travel at $c$.
Gravitational waves are the contraction and expansion of spacetime itself. There is nothing that can get in the way of how spacetime reacts with itself, there is now way to slow it down.