Oh ... forget about the shock collars
That is pup abuse
I have the same problem once in a while with my Mike
and it's best you get a handle on it before the other one gets older because take it from me
The other one will join in soon enough and it will be a midnight chorus going on in your house
The way to stop the 4 am barking is to stop the barking all together
A barker during the day is going to be a barker at night too