He actually mentioned the once that he sleeps in small bursts to cover this stuff, as there are various stretches where he doesn't have such people. The Outsiders particularly he has thrown at outside Gotham stuff/assembled as a post death instruction/that sort of shmear.
On your list of sleuths..
Owlman, the outsiders one, is lacking in up to snuff physical capacity as far as not getting killed. Dibny does not get his powers, and thereby is massively lacking in physical capacity as far as not getting killed. Mid-Night isn't as good a detective as Batman, barring medical forensics, and that's kinda specific, Terrific is significantly impaired by the tech limitation, though of this crowd he'd do the best job. And detective chimp, again, has the physical oomph of a chimp.There were a bunch of sleuths in the pre-Nu52 DCU. Mr. Teriffic, Owlman, Ralph Dibney, Dr. Mid-Night, Dectective Chimp.
But yeah, the people Batman trained could sub in for him.