I'm pretty sure that the singularity is not the fact that it's a point, but that the gravity is so high that it wraps in on itself. i.e. that spacetime has a hole in it.

Because once gravity is that high going any higher has no meaning by any physics currently known. So by that definition once you crossed the event horizon anything inside has no meaning - and that is the singularity (i.e. the calculations of relativity have an infinity there, which is the singularity, not the mass in a point).

Also I did sort of assume that if matter can not collapse to a point a black hole is impossible. It does not appear that a quark star could be a black hole. And nothing is known about the other candidates listed on wikipedia (Preon star and Q star), but there sort of is the assumption that they could not make a black hole.

The article referenced for Q stars says 1.5 Schwarzschild radius, so it looks like to make a black hole you need a point mass.