The problem could be as simple as boredom. What is her regular daily routine like? Does she spend a lot of time alone? Go on regular walks? If you can't make time to exercise her, one good solution is to adopt another dog as a playmate. It really makes a big difference for a dog to have a pack and playmate with so many households being empty during the work and school week.
It could be a neuro issue. Sometimes dogs chew due to nerve pain or sensations they just don't know how to deal with any other way. Has she ever had allergy related issues before? If not then at 11yrs old I'd be looking for another diagnosis. Plus the fact that it's centralized just to the spinal area seems neurological too. A neuro consult couldn't hurt.
Have you looked into the possibility that she could have an OCD? Dogs can suffer from Obsessive Compulsive Disorder just as humans can, and sometimes it manifests itself in self-mutilation. Sometimes they will chew on their own paws, or on their tail, it just depends on the individual.
Maybe try a diversion therapy? Find something that she really, really likes in the way of a toy, or something that really holds her interest. When you catch her chewing on herself, divert her attention away with whatever her favorite thing is, and take her mind off the chewing. Every time you catch her chewing on herself, divert her attention with her favorite thing.
Has she been spayed? Sometimes cystic ovaries will make them do some REALLY strange things, and by spaying them, it levels out their hormones and the behavior stops. Sometimes hormonal problems occur even in spayed females. Have they tried hormone therapy (like, say, Ovaban) to see if it makes a difference? Maybe even a mood elevator (Elavil?) could be tried to see if perhaps it's her nerves that are causing this?
When you changed her diet, what diets did you try? Sometimes, if it's an allergy, it doesn't have to be an allergy to an actual food, it could be an allergy to an additive in the food. It could be a dye, it could be a preservative, it could be a flavoring that is sprayed on the food after it's manufactured. Have you tried a diet of home cooking or even the BARF (Biologically Appropriate Raw Foods diet? That way, she'd be getting JUST food and nothing used in the manufacture of prepared pet food.
If I think of anything else that it might be, I'll post back. These types of conditions are some of the most frustrating to attempt to figure out, because the possibilities are practically endless!
Ghilly