I hear you. My wife and I are trying to corral a pregnant little stray who comes around but she won’t let us get near her.
We have a male hanging out on our doorstep, “Mr. Strangecat,” who really wants to move in with us. (Our two are spayed and neutered.) I feel bad for him, especially when the weather is unpleasant, but we don’t want another cat and who-knows-what vet bills!
From experience, the stray is a lost cause. Once the kitten drops, find it and nurse it as a pet. The mother will NEVER domesticate.
Mrs. Tweezers and I had the good fortune that a pregnant stray (who was probably responsible for a large part of the feral cat population in our neighborhood) decided to adopt us. We found good homes for her babies and got her spayed and registered.
She has turned out to be a good kitty. And I don’t say that simply because she’s decided I’m “her” hoomin. :)