Dog has recently developed a chewing problem

Question
We have a rescue dog from the shelter that is 14 months old.  She's a mutt, and we decided from the beginning that we wouldn't crate her.  She was housebroken really fast, and we had no issues until she turned about one.  We got her when she was 5 months.  Since then, when we leave the house she'll chew anything that she can get her little jaws on.  Recently its been my shoes.  4 pair in 4 days!! We can't take much more of this, and my fiance is ready to crate her.  I would prefer not to have to do this, but we really are at the end of our rope and patience.  The odd thing is she'll go days at a time without doing this, and then go on a rampage.  We can be gone 7 hours, and no issues, or 20 minutes and she's destroyed 3 DVD's a pair of shoes, dumped the bathroom garbage, etc.  She has plenty of bones, chew toys, kongs, etc....   Any suggestions would be GREATLY appreciated.

Answer
If you're not going to crate her you must at least restrict her to one room when you are gone. And dogproof it. Those things you can't move coat with bitter apple or hot sauce.

It sounds like she likes stuff that has your smell on it, get three sets of toys for her and rotate them. First, put the first set in your laundry hamper overnight or even for a couple days. Give that set to her just before you leave and put the next set in your hamper. After a couple days, put the set she has in the dishwasher (low heat, some of them melt), the third set in your hamper and give the second set to her. A few days after that put the clean set in your hamper, and so on.