I think you are going to keep on breaking center drills or spot drills; the tip grind right at the point is not strong enough to take the forces need to make it cut material that hard.
What you could try is drilling a small pilot hole with a carbide drill then machine the taper with a very tiny tool; the very tiny tool could be something like a 1/8" two flute end mill.
I have used this approach on hard stuff but not that hard.
An open mind is a virtue...so long as all the common sense has not leaked out.