I wouldn't be crating when it's possible to supervise. Sure, encourage the pup to go into the crate, but don't lock him in if you don't have to.
When you say he is screaming when you leave the room, are you talking about leaving him in the crate, or leaving the room and closing the door to prevent him following?
"Classic puppy shredding"? This is the time to teach your pup what toys are for chewing and what toys should be played with gently. If the pup starts destroying plush toys, for example, take the toy away and replace with something meant to be chewed. Supervise play with toys that are easily destroyed. This will pay dividends when he doesn't rip up your clothing because he has been discouraged from chewing on cloth. Raising a pup is being intimately involved with him, being observant, giving direction, with the goal of having a pleasant companion. A pup in a crate is learning nothing. Use the time you are home with him to teach him how to behave. Use the crate for his safety when you can't be there, but with the goal of being able to trust him out of it, maybe in a "dog proof" room, but somewhere he can be comfortable, warm, and ideally able to see outside. It's early days, your pup is not used to being alone, of course he wants to be with you, especially when you are home and he knows you are there. Pups generally relax when they are able to be with you.