I think you have it backwards. From the POV of someone near the Event Horizon, other space speeds up. Galaxies begin to spin at noticeable speeds.... But the black holes would appear to be approaching each other at "normal" speeds.
I suppose nothing but gravitational waves can escape the even horizon — or, rather, gravitational waves are born near / around it, because the black holes bend the space enormously.
OTOH whatever else may be outside the black holes near the merger and count towards their mass for astronomical purposes, such as accretion discs, should be much lighter weight than what's inside the event horizon.
Gravity does action at a distance. That's its thing.
The reason these waves are not generated from inside the black hole is that, to us, time stops there. For example these black hole mergers aren't actually merging, they are getting closer, and then they time dilate out of existence.
> Gravity does action at a distance. That's its thing.
Why does it need to travel in waves at the speed of light? If one mass moves, a distant mass is unaffected until the information reaches it. That's the opposite of action at a distance.
Your question is confusing. Action at a distance does not imply going faster than light, it means there is some sort of field connecting the two things.