Lets see, how many ways is this whole discussion wrong????
1. the only point mass is the singularity in the middle of a black hole

What good is General Relativity if Newtons laws are wrong?

2. you refuse to allow infinite density, but insist on zero size

The "size" of a point mass does not converge at 0.

3. you refuse to allow quantum mechanics yet require interactions that are
clearly in the quantum realm

Quantum mechanics brings down alot of concepts from Newtonian
mechanics and Classical physics. When considering NEWTONIAN MECHANICS,
it is not valid to invoke QUANTUM MECHANICS to explain away logical
inconsistencies with the former.

4. contact forces??? how can you have contact between two zero size objects?

Any body in Newtonian mechanics is considered the integral sum of its
containing point masses. This is basic physics and quite a fundamental
assumption. Otherwise, is space quantized? Is mass quantized? Does the
problem go away? No. The continuity of space and mass density IMPLIES
the existence of point masses - so then explain the mechanics of point
mass collisions without invoking the quantum model - a fundamentally
different and irreconcilable model. Claim your relativistic
stress-energy tensor allows for a discontinuous mass density across a
locally Minkowskian 4-manifold and maybe, just maybe I'll believe you.

5. there can be no empirical evidence of a situation like this

There doesn't need to be any evidence if it is a mathematical (albeit
quite trivial) analysis of Newtons laws. They don't work for point
masses as you can find yourself faced with a LOGICAL FALLACY (do you
know what that actually means?). Newtons laws by themselves are
inadequate or incomplete at best. Or maybe they are just plain wrong.


6. two object can't occupy the same point in space at the same time

Where do Newtons Laws prohibit this?

7. what happens to the gravitational attraction at zero distance?

Gravitational attraction is not explained with Newtons 3 Laws. Newtons
gravitational law is provably wrong yet it suffers not the fate of the
first three, but a much worse one. "Force at a distance" is one of the
most blatent signs that the Newtons first law is WRONG. The state of
physics today is a reflection of the propagation of these fundamental
mistakes.

8. what happens when the two event horizons overlap on the two black holes
that must be colliding?

Relativity is irrelevant when considering Newtonian Mechanics.