High-prey drive and anxiety

Tldr: dog is killing animals outside and worried he will kill my indoor cats, on top of having severe separation anxiety. considering behavioral euth

Very long story short: I have an ~11yr neutered male large mixed breed dog with an incredibly high prey drive and separation anxiety. I have one other dog who he gets along well with. I have four cats.

I did not intend to adopt this dog – 3 years ago I volunteered to foster him to stop him from being euthanized at my local shelter (I live in the south and there is incredible overpopulation – he was a stray that was going to be euthanized because of lack of space). After I took possession of him, the rescue group ghosted me and I had to assume ownership. I intended to find an adopter but ended up keeping him due to behavioral issues (and falling in love with him, of course).

My household is kept separated between dogs and cats. There is always at least 2 shut doors between the dogs and the cats due to my dogs prey drive. The dogs never see the cats. This has been working well.

However… My dog has killed 3 cats and several possums in my yard. These are all stray cats, of which there are plenty in my neighborhood. I never feed the outside cats and scare them away when I see them on the property for their safety. After the first cat, we began muzzle training him and only letting him in the yard with a basket muzzle on. He has never acclimated to the muzzle despite we extensive muzzle training and manages to get it off regularly, which is how the other attacks happened. He is only allowed out with supervision and we check the yard for animals before letting him out but he has still managed to find critters.

He also has extreme separation anxiety and had to have an $8k surgery to remove cloth from his intestines in March of this year. He is on high doses of medication for his anxiety which has helped, along with training. But it has not mitigated it completely. When left alone, he will destroy and consume inedible things such as couch cushions or plastic bags, maybe about once a month. We try our best to dog proof the house as much as possible but he will find things that I wouldn't have even expected him to find or eat. I cannot crate him because he injures himself out of panic. He has multiple broken teeth and cut his mouth and tongue trying to escape. I have even gotten an indestructible kennel which he managed to injure himself in. We only have one veterinary behaviorist in my city and the wait list in several months.

He used to be aggressive towards strangers in the home but we have overcome that. He is dog-selective, but generally aggressive towards strange dogs.

Most of the time, he's fine. He sleeps when we're not home and is fine. Then he will eat something and I am full of stress that he will need another surgery I can't afford, or he will manage to get his muzzle off and attack an animal in the yard.

I am extremely worried that something will go wrong someday and he will manage to get to one of my own cats. I love him with all of my heart but am beginning to resent him. My boyfriend is not as animal savvy as I am (I am a vet tech and work in animal welfare and have for years. He loves animals but is not as experienced.) He gets incredibly upset when he attacks an animal (understandable) and resents him more than I do for it. He thinks he's being an asshole while I recognize that he is just being a dog with prey drive and anxiety issues.

He killed another cat in our yard last night and I don't know what to do. It is at the point that I'm considering behavioral euth. I very much doubt I can rehome him as he is a large senior dog with human and animal aggression and separation anxiety. But I don't know if me or my boyfriend could forgive ourself or him if he attacked one of our own cats. Our household is working being separated but I am so stressed that a door will be left open and he will kill them. Or that he will eat something and need another surgery that I simply cannot afford, I am still paying off the loan for his $8k surgery.

Any advice is welcome.