Would some condition, that the dog must be muzzled at all times whist on common property, be a compromise?
Yes, and the offer of such a compromise would probably get you past the ban on pet bans – and would surely be rejected by the dog owners. I just worry about any cats that might stray into its zone. Apparently it’s not illegal for a dog to attack a cat that is in the dog’s territory, but it is if the dog is in the cat’s area or on common property.