We had a trainer over yesterday to help us work through this separation anxiety. It was a good visit, reassuring and informative. The bottom line: there's no magic cure. Helping Lola overcome her anxiety will take time and patience.
Our plan is to essentially desensitize her to the cues that we are leaving and gradually get her comfortable with being left alone. This means that in the meantime we cannot leave her alone, because each time she goes into panic mode that causes us to go backwards in progress. So, we're working on finding a place where she can be happy and calm while we're away. That's the difficult first step, but we have some ideas and leads. Hopefully one will pan out.
We are also taking her in to the vet to get a prescription for doggy prozac. Her case is bad enough - she cannot be left alone for any amount of time - that medication may be helpful. It was recommended that we give her about four weeks for the meds to build up and start having an effect before we start the training. Yes, this will be a long process.
We also decided that there's not much point to using the crate. That causes her to panic more and she breaks out anyway.
We discussed getting a second dog. Our trainer basically said it's a gamble, which is what I was thinking. A buddy could help with Lola's anxiety. On the other hand, a new dog could actually develop anxiety from being with Lola. That would not be a good development! So it seems the best idea is to get Lola to a better place before adding a new dog. That makes me a little sad, because I was getting excited about that possibility, but we have to accept the reality of our situation.
That's the basic summary. Obviously, we discussed it all in far more detail. We worked on some other things too, like loose-leash training. She did well and I can see us making good improvements there. Overall, I fell clearer about how to approach this problem. I'm happy to share more if anyone's curious.