When there was a mamma cat and her kittens using my parents' front door area for a potty, I hit upon something that worked but with all the cats you have, I don't know if it would work for you: I cleared out all the mulch and all the cat mess, and put down the large nugget mulch, the kind that has pieces about the size of a TV remote. Then I bought several cheap containers of red pepper flakes, and spread them on top of the mulch. This took care of the problem. The large nuggets are unstable under their feet, and of course they don't like the pepper smell.
But this
should not be your problem to solve.
@bobm, have you tried talking to some of the area vets, to see what they would recommend? Surely they are not all on the same "save the strays" bandwagon.
I don't like the idea of shooting stray cats, but in some cases, there doesn't seem to be any other solution. Feral cats are really hard on the song bird population. I guess killing them humanely is a choice we may have to make to save other species, and, of course, to keep our property from smelling like, well, tomcat teen town. Could you even shoot them with a gun in your neighborhood? You don't want to poison them; valued pets might be killed.
Good luck on your efforts.