We have the same problem here with Fox. This past summer a female denned under a neighbor's cabin. He doesn't want it there but this is one smart little fox and she lives up to the character of being wily.
Over the summer months she managed to desimate the local flocks. Luckily we didn't loose any so far as our birds do not free range, their coop and run are fort Knox and I have a hot wire around the whole coop and run.
We saw this fox on several occasions on our property. She is big, healthy and beautiful but she has to go. I finally made contact with a conservation officer who said take her out. There is just about no way to trap a fox. They are too intelligent and crafty, so I am glad to hear that you are prepared to use extreme prejudice on this animal because she will take the rest of your birds if she has a chance.
If you are prepared to hunt her, I'd look about one of those electronic lures that duplicated the sound and action of a wounded rabbit to draw her in. You are going to have to out fox her and it will not be easy. We got the word out to shoot to kill but nobody has seen her recently.
I truly sympathize with you not wanting to kill it but knowing you must. The fox is just being a fox and trying to feed her kits. The first words out of my mouth to the MDC officer was, can't you please trap her and relocate her on conservation owned property where she won't bother anyone. He said they seldom had luck trapping a fox and she has proven to be a nuisance animal to farm livestock.
Good luck with your project. I hope you get her before she kills again.