This might not literally be what you are aiming for, but everything we see or hear is from events before the horizon forms. And the gravitational waves are also emitted before the horizon forms.

Which means there are events in those stars and between those stars that happen after the waves we've seen are emitted. All the way in the center of the star we called the first black hole, and all the way in the center of the star we call the second black hole and in any part of the space in between.

So we do know what that looks like. And we can solve for it. And you do see the two stars orbiting each other. No singularities. No event horizons. Just time dilated signals coming out towards us.

So its "inside" in the sense that there are no holes or missing parts. It's just that the pre horizon events are very time dilated so a little bit of them covers a lot of our time. And at least those are the most scientific parts.