I feel for you... we have no leash laws here either, and a dog must attack twice before the procedure for declaring it dangerous and forcing containment can be started. However, should it attack your chicken or duck, you can kill it on the spot. Insane.

Maybe have the sheriff tell the owners of the dogs you've already encountered what he told you about shooting them, and that you intend to continue riding there. Doesn't do a thing for the new encounters though. That's the frustrating part; we shouldn't have to deal with loose dogs AT ALL, they should be contained.