Have you tried going out for mini periods and coming back before she can do anything destructive?
It could be that she is not used to being alone and has to learn to understand that you are coming back.
And yes, you're right to not make a big deal about coming and going.
I have a 12 week old puppy and he has pretty bad separation anxiety (and HATES the crate). So I have been leaving him for 10 mins at a time, coming back, ignoring him for a while and then once he's calmed down going to greet him.
With the crate I have completely given up on locking him in it - it is now just his bed with the door open.
However, if you can get her to sit peacefully locked in the crate with you in there that's good.
And if you wont give her treats then training her will be very challenging - if she is on a diet you could give her some of her meal normally and the rest as treats. The hungrier she is the more impressionable she'll be!
You're one of the wonderful rare people that will take an older rescue dog - not many people like to take them on!