Muzzling on a farm/ranch might not be a good idea for safety reasons. It could get caught on something and trying to keep him under watch at all times is probably impossible :(
Sorry to hear about the sad demise of your kitty, QT. Rehoming your barn cats wouldn't solve anything, especially since rats/mice in the barn would definitely increase :rolleyes:
I hate to say this, but I doubt he'll ever 'get better.' In fact, if I was analyzing a human serial killer, I'd say that he's 'increasing' as he's becoming more confident about his position. He went after 2 cats in two days --the one that you managed to save. Every other death had been spread out. It will likely only get worse. :(
You could likely have to worry about the other dog that you mentioned. It is possible that he 'taught' yours that killing a cat was 'fun' or 'acceptable'.
Wish I could give you sound advice, but I have none. Would a {{{{{{{{{{Hug}}}}}}}} help at all? :)
toodles