That's good and, hopefully, over time these issues will resolve. You should dog proof as much as you can and limit the areas he can be in unattended. The Greyhound we adopted had SA issues so he had to be crated when we were not home. Eventually, I would leave the crate door open but had a baby gate up to keep him in the kitchen and family room area and leave him with the radio on and a couple of stuffed Kongs. As time went buy and he got used to us, the house, routines, etc we were able to leave him out.
Thank you all for your comments. No, I will not be shipping him off to anybody else. We have pretty much decided to adopt him even as a chewer.
Also make sure the bone is raw, not cooked. Cooked bones can splinter and harm your dog.
He does sound like a big sweetie. I love big dogs, my daughter's service dog is a big labradoodle (labradoodles love to chew by the way). Do you know if he can handle a bone? Almost every day I give our dog a big marrow bone to chew on. It keeps his brain occupied and lets him get out his need to chew. I may also recommend punishing him immediately after he tears a hole in something. Such as a time out in the crate. The best way to do work on this is to prevent it though. Just make sure when he has the bone you keep an eye on him to make sure he doesn't choke or crack a tooth. You could always hire a trainer to help you. They will usually come out to your house.
Give him some time! You said it's been two days. Who knows what his life was like before now or how many places he's been bounced to and from. He needs time to get familiar with his surroundings and your schedule. Try teaching him new things/tricks. He'll be busy learning and it'll give him an outlet for his energy. Get some baby gates and block off rooms you don't want him in unsupervised.
Yes, exercise is important. Sounds like a handful. Have had a couple of Greyhound rescues like that. They did not have free reign in the house, used the crate also. Had to dog proof, as much as I could.
Have you tried a couple of stuffed Kongs or an activity toy?