Deformation of Schwarzchild radius of two approaching black holes I'm trying to visualise merging black holes. Here's my impression of a single black hole:

Green is the strength of gravity outside the Schwarzchild radius, blue is the strength of gravity inside the Schwarzchild radius, getting stronger as it gets darker. Red is the approximate location of the Schwarzchild radius (just there to make the image look nice). The Schwarzchild radius is 100U, where U is any unit you think makes sense.
Here are two hypothetical identical black holes approaching each other on a head on collision course:
150U apart

100U apart

90U apart

~87.74U apart

75U apart

50U apart

1U apart

Is this an accurate visualisation in terms of the black holes not merging when they're at double the Schwarzchild radius from each other and having a pocket between them where the gravity is less than inside the Schwarzchild radius? It appears that in my example the Schwarzchild radii just touch when the black holes are ~87.74U apart from each other.

Additional information
I'm trying to visualise it the way it's done at the Lagrangian point Wikipedia article.


Instead of the Sun and the Earth, I'm using two black holes. A comment links to an article showing that the Schwarzchild radii are attracted to each other and stretch out. Why wouldn't you get an L1 point between them like for much smaller bodies?
 A: There's a lot to unwrap here.  As noted in the comments, the OP's decision to use Newtonian gravity to emulate the situation will not be perfect, but it actually is enough to get a qualitative understanding of what's going on.
But first, there's a problem with the series of images in the OP.  The thing being plotted in that series is the magnitude of the Newtonian force from two point masses.  Specifically, if the point masses are at $\pm \vec{a}$, those images are evidently showing
\begin{equation}
  |\vec{F}| = \left| -\frac{\vec{x}-\vec{a}} {|\vec{x}-\vec{a}|^3} -\frac{\vec{x}+\vec{a}} {|\vec{x}+\vec{a}|^3} \right|.
\end{equation}
The concept of force doesn't extend very nicely to General Relativity.  Instead, what we should look at is the much simpler Newtonian potential
\begin{equation}
  U = -\frac{1} {|\vec{x}-\vec{a}|} - \frac{1} {|\vec{x}+\vec{a}|},
\end{equation}
which looks like this:
.
The specific reason the potential is more interesting is because in linearized gravity, the potential is basically the time-time component of the metric — which describes "how fast time is flowing".  Don't get too excited about this fact; it's a poor approximation right near the horizons.  But at least when you're at some distance from the black holes, it's not a bad way to get some intuition.
As the OP's images show, the forces cancel out halfway between the two masses, but the image here shows that the potential is never zero in between (like it is at infinite distance).
Physically, the force diagram shows that an observer halfway between the two holes would not be accelerated toward either one — which is what symmetry demands.  On the other hand, the potential diagram shows that an observer halfway between the two holes would experience time flowing at a different rate than someone very far from the black holes.  And in fact, if you go the same radius from one of the black holes, but in any other direction, you have a larger (less negative) potential.
So while the OP's images suggest "a pocket between [the masses] where the gravity is less than inside the Schwarzchild radius", the plot of potential actually shows that having two masses really does "increase" the "amount" of gravity.
Having said all this, I'll note that the conclusions drawn from all of this are valid, but the methods are very approximate.  In particular, one of the main lessons of Relativity is that coordinates don't mean very much, and we have to be very careful if our precise results depend on our choices of coordinates — as they do here.

While not too closely related to the topic of the question, it's also important to note that when looking at Lagrange points, the thing being plotted there is an effective potential, which accounts for the centripetal force experienced by an object orbiting around the center of mass with the same period as the two main masses.  (I think wikipedia does a poor job of explaining this.)  But since the OP is talking about a head-on black-hole merger, only L1 exists, since there is no relevant centripetal force.  And the L1 point is precisely what is seen in the OP's images where the force goes to zero in the middle — and equivalently in the plot of potential above, where the potential reaches a level point right between the masses.

Finally, I have to point out that some of the comments are misleading or wrong (particularly some on the now-deleted answer).  Specifically, the paper @safesphere linked is old and has been superseded by this one, which was created using much of the same code.  Most importantly, those results are consistent with the visualization in the first youtube video linked from the now-deleted answer.  The whole point of both of those papers is that the shape of a constant-time slice through an event horizon depends on how you slice it — which is a mostly arbitrary set of choices.
On the other hand, the point of the video (and the paper that goes with it) is to show what photons passing near the binary would do as (literally) seen by a distant observer.  The video does not actually show any horizons, because one cannot actually see a horizon, and therefore doesn't need to show the horizons extending toward each other.  What it does show is the shadow of the horizons.  It is essentially correct (to the extent that any finite computer simulation can be), and is still considered the most accurate simulation of what a merging binary black-hole system would actually look like visually.
[I should note that I was a grad student in the group that produced the first paper when it was produced, and a post-doc in the group that produced the later papers and video at the time they were produced.  It's all work from the same collaboration.  Though I was not personally involved in the work, I'm quite familiar with all of it.]
