Why are you going outside everytime he barks?
You really need to look at this quickly and decide whether he needs to go back to @purplequeenvt
You got an LGD to protect you alpacas and poultry.
LGD's BARK!
They bark as a deterrent first!
If the predator is bold enough to proceed to your livestock or poultry then they kill.
Right now he is in a new environment. Prior to his being there you had an idea what was out there but no real concept of how many critters are on the move. The heavier the load the more barking.
There are seasons where they bark more. Like this time of year. As well as sound carries with no leaves on trees and colder air.
Two things-
1.He is going to bark PERIOD! Just because you don't see, hear or smell it doesn't mean it isn't out there.
2. If you do not let the LGD be a LGD you will frustrate and exacerbate the dog. This allowing your LGD to be what you got him for is critical to the trust and best interest of the dog.
Not trying to be a jerk here but if you cannot handle the barking then you need a different type of guardian. If your wife is frustrated and irritated she will end up hating the dog, she will not respect the dog. When these dogs are not respected and they know there is resentment they will respond, mostly in negative ways.
I have seen this before and it can cause a great deal of strife.
Not everyone is cut out for owning a LGD. If your wife is already this upset with him being there for a few days and he hasn't even fully adjusted... this is not a good sign.
A good example- I can hear my dogs inside the house but I could not hear why they are barking.
A few minutes ago I took Rita out... off in the distance I hear coyotes... I also hear the cows (they are about 1/2 mile away)... not sure if the cows are calving or if it is the coyotes upsetting them but anyway my dogs are going nuts. They go quiet and stay quiet then they get set off. This is what they do.