I don't know how easy neutron stars are to find. I also don't know how easy binary neutron star systems are to find.

I do know we've been getting gravitational waves from all across the universe every few days from neutron star collisions and black hole mergers for the last few years. But that is a sample size of billions of cubic light-years of space. We're talking trillions of galaxies. A typical galaxy does not have a neutron star or black hole formation in any predictable way. I refer to the milkdromeda galactic merge for the most likely next neutron star collision anytime soon.

Now... engineering a black hole? That's bonkers. I would pay to see that. Someone get kurtzgesagt on that. Would become one of the most extreme science experiments possible.