I realize that you don't give her the run of the house.
I didn't give Sadie the run of the house either. I left her every day in a gated in area with a peanut butter stuffed kong and numerous chew toys around her. She was also done teething but would start chewing on things as soon as we left the house. If she was outside (we left her outside for a couple of days when she had severe diarrhea), even with toys and things in the yard to amuse her, she chewed on our newly built cedar stairs.
Sadie not only underwent obedience training, but training in agility and flyball.
It probably had nothing to do with the training, but more the maturity level of the dog. Right around the 8 month mark they're in their rebellious teenage stage of life, at which time you often have to treat them like puppies again. Even though my dog chewed things and your dog does different things that are destructive, its more or less the same behavior.
If you've done training with your dog before I don't think that its necessary to do it again, unless its something you enjoy or she's never had any professional training. I believe that every dog should go to puppy class or basic training.
I'd go back to crating until she's older and can handle the responsibility of being loose (somewhat) when you're away. If you didn't crate train then I'd severely cut back the space that she's in when you're away. I'd either consider crate training, getting an x-pen or blocking in into a small area, maybe 4 ft x 4 ft.
You may also want to practice NILIF (Nothing In Life Is Free), which will help her learn her place in the house.
http://k9deb.com/nilif.htm