Take an ordinary brand new cleaning sponge, soak it in meat gravy , and then compress that sucker into the smallest container you can, down to the size of a golf ball.
Stick it in the freezer overnight.
Run a little warm water on the container, slide out that compressed frozen sponge and chuck it over the fence in the dark,(two or three are better and quicker than one but also more suspicious)
In a week you will have no more dog problem in the neighborhood, and most owners and vets will think the dog just ate the sponge, if they are ever discovered.
My farmer friend says the owner should bury them, which is why he won't shoot them. The trespassing dogs usually swallow the frozen sponge in one gulp.