Why do you think a muzzle is better than a bark collar?
I don’t really think a muzzle will stop barking; certainly a basket-style muzzle will not. And not sure I’d really want to walk a dog in a muzzle that kept their mouths closed. They need to be able to pant, even if it doesn’t feel warm.
Positive reinforcement isn’t the only way to teach things; a leash is negative reinforcement, for example. I don’t know that a bark collar is what I would use in these situations, but I wouldn’t be against a human-controlled e-collar used correctly, especially in situations where positive reinforcement doesn’t work.
That being said - I think the hound sounds like a relatively easy fix. Training, time and exercise will likely improve his leash manners.
The Aussie is another story; I am not sure that I would attempt to “fix” dog aggressive behaviors while out on a walk, and certainly not while handling another dog. Unfortunately, I think that would require more intensive training - the nothing in life is free type training.
What are your options for exercising the dogs off leash? I definitely think regular, hard exercise can solve a lot of issues. Tired dogs are easier to work with than those with boundless energy.