Mental exercise = Teaching obedience commands or tricks, playing hide-and-seek (using toys or food), etc. Physical exercise is great, but absolutely nothing tires a dog out like a good session of mental exercise. Clicker training is fabulous since it really gets a dog thinking.
How old is she? Has she always had some SA?
For a dog who has destroyed a crate, and especially if the SA behavior has been going on awhile, I really think getting some medication from the vet to take the edge off and then working on retraining is the way to go. You have to lower the stress level (with the medication) so the dog can be relaxed enough to relearn good behavior.
ETA: If she's food motivated then even with food allergies I'd always leave her with a food treat. You can take some of her regular food (moisten it if it's kibble) and stuff it into a Kong and freeze it. A frozen stuffed Kong will keep most food motivated dogs busy for quite awhile. And most experts believe the worst time for a SA dog is the first 10 or 15 minutes after their person/people leave. So if a treat can keep her busy and distracted for that time period it can really help.