You cannnot leave a dog muzzled when you leave it alone with other dogs., and I have never known a muzzle to stop a dog barking other than a cruel strap muzzle which holds their jaws closed.
The antibark collars that spray a citrus liquid when the dogs bark are quite good, look on ebay they are cheaper on there. Ther are others, but the dogs soon get used to them. If you intend keeping this dog for any length of time then try getting him one, and see if that solves the problem.
I would seriously suggest that you make arangements for the dog to go to someone else, as it is obviously upsetting the balance with your own two. There is nothing worse than neighbours who are anti dog barking (can't really blame them). Although you are doing it a favour, is it really worth the grief or fair to your other two? I assume you are getting stressed out with the situation and they will sense that and think it is their fault. He is obviously not happy, and needs to be with someone who can be with him most of the time, and spend time teaching him to be left alone.