In my experience, whether or not the 'leave them to it' approach works depends very much on the dog's personality and temperament.
If you have a dog that attaches strongly to it's family then they struggle with just being left. Lots of breeds that came about doing jobs in which a close bond is required (e.g. gun breeds, of which the OP's pup is one) are like this. Am not a massive expert on wolfhounds, but I suspect they may also be of the type to strongly attach to someone.
If your dog is more of an independent nature - terriers, bred to do a job by themselves with minimum human input are often like this - deal better with being left. (Note, this is not about how much the dog loves you, just how happy he is to be apart from you)
My springer is an attached one. When he was young he would howl if I left the room. I am not one for tough love so never asked more of him than he was happy to give so I had him in the bedroom to sleep. At nine months old now he has naturally increased his independence and distance from me. As I type he's taken himself off into the kitchen to sleep. Yesterday he spent most the afternoon sleeping alone and was happy when I had to pop out.
If I compare him with a friend's cocker: they had to leave her for short periods from a young age. They would often come back to find she was in a real state, panicking and upset at being left. They kept at it and she was about a year old when she finally settled to being alone. My conclusion is that both dogs will have taken about a year to be happy alone, but in my case he never had to be upset while getting there. I am really glad I never forced the issue and have left him to come at it in his own time, without any distress.
Obviously all dogs are individuals so there will be terriers that strongly attach and spaniels that don't. It' about knowing (finding out about) the dog you have.
Anyway, great update from OP so finger's crossed they are through the worst of it.