If two black hole event horizons overlap (touch) can they ever separate again? Hypothetical question based on my understanding that two event horizons that overlap (touch) can't ever separate again:

Imagine a 1 billion solar mass black hole (so the event horizon is massive and very gravitationally weak) is travelling at a velocity of 0.9c through empty flat intergalactic space; now imagine an identical 1 billion solar mass black hole travelling at 0.9c but in exactly the opposite direction so the two are heading roughly towards each other. The black holes' paths, once all the space time warping is taken into account, aren't on a direct collision but the outermost edges of the event horizons will just 'clip' each other, ordinarily only overlap for a fraction of a nanosecond as these two bodies are travelling at such incredibly fast velocities and in opposite directions to each other.

So firstly, am I right in thinking that if two event horizons overlap they can never 'unlap'?

Secondly, what would happen to this incredible amount of momentum of each other the black holes? Would it just get instantly turned into gravitational energy? Bearing in mind when black holes normally merge, it happens very slowly as black holes slowly move closer and closer together over millions of years giving off gravitational energy as that happens, so not in a fraction of a nanosecond as in this case.

And thirdly, what would this look like? Would the event horizons remain fairly spherical and the radiated energy just insane or would they stretch and warp into a kind of long thin elastic event horizon as they shoot past each other and then over time slow down and snap back to each other?
You have already got some good answers, but I'll just try to provide one more intuitive solution on why the event horizons will never separate again if overlapping each other:
First, imagine a speck of dust that comes inside the EH of a black hole. I believe we'll agree this speck can never escape the black hole, because nothing can come back from behind the event horizon.
Now, imagine the same speck of dust, but inside the overlapping parts of the EH of two black holes passing each other. This speck of dust will never escape any of those two black holes, because it is inside the EH of them both. If these black holes would be able to separate again, the speck caught between them would obviously escape at least one of the black holes, after being behind it's event horizon.
Since this can not happen, the two black holes will be united from the point their event horizons are overlapping, no matter their speed.