Training is not the same as behaviour modification. Teaching a dog not to pull on a lead will not cure fear aggression, counter conditioning will. Obedience training won't.
Wrt the halti, your trainer, if they were halfway decent should have gone through techniques with you that get the dog to associate the halti with something good. You can't just put on a head collar and expect the dog to learn to love it if it doesn't bring good things to it's life.
Also walking on a Halti is not training. It's a quick fix and useful tool to aid training, but it's managing a problem, rather than solving it.
Did your trainer do any actual training with you? Did they suggest anything other than a halti? There are many anti pulling harnesses out there, some work for some dogs, others don't. A front leading harness is the kind I prefer.
Wearing a muzzle, along with muzzle training is fine. Advisable even.
Avoiding triggers, at least until the dog has had a chance to recover is sound advise. You shouldn't have been forcing him into situations that he was uncomfortable with. That would only ever have made the issue worse. A decent behaviourist would show you how to slowly introduce scary situations at a speed at which the dog is comfortable with. BAT wuld be great at helping with the dog aggression issue. Ask if the behaviorist is experienced with BAT techniques.
You've had one spectacularly bad trainer, by the sounds of things. Go and see your vet and ask to be referred to an APBC or APDT registered behaviourist. I can guarantee they'll much more competent and helpful.
Wrt what you said about avoiding rescue centers, not all of them are the same. I know of a few small rescues that take in dogs like this, rehabilitate them and give them a good life. Not all rescues are run from large, over filled kennels.
You don't have to rehome him. Work with a proper behaviourist.