I know you don't intend to mistreat this pup, but I think that leaving a new puppy in a room all alone is downright cruel. He's been taken away from everything and everyone he knows, put into a totally strange place with strange people, then locked in a crate where everyone leaves him in this unfamiliar place by himself.
I think puppies need constant assurance, like any baby, that everything will be okay and that they are safe. How can they feel safe in that situation? How can they be confident and happy when abandoned like this? To me, it's just wrong.
At least move the crate into your bedroom, close to your bed, where you can reach down and touch the puppy when he gets scared or upset.
We often take new puppies into our bed, just for the first few days, to let them know that they haven't been completely abandoned. It's also a good way to prevent accidents during the night, since they will get restless, which wakes us up, when they need to go out.
If your pup knows he is safe and protected, you will all get some much needed sleep. I don't feel this has anything to do with separation anxiety. It's just a very upset puppy who doesn't know why he's been left alone. That situation had never happened to him in his short life until he went to live with you.
Try looking at things from your puppy's perspective. It might save all of you a lot of grief in the future.