Separation anxiety can be a tough problem to solve. Getting another dog may or may not improve things, as I am sure you know. Do you by any chance have a secure outdoor area where you could leave them? That worked for us in summertime. Although our girls were not house destructive they were much happier to be outdoors in a large run with sun and shade and water. One alone would have preferred to be indoors, as I have since discovered.
BTW, your Loki looks like a real sweetheart!
We tried to put her outside but she starts that screaming and it scares the neighbors and made the kids cry that live behind our house. We left her for 10 minutes and I walked home the back way to see how she was doing, this was when I discovered she can hit probably 110 decibels with that scream, or more.
She also has the bark of a 100lb German Shepard! How something that weighs 45lbs can have such a deep powerful bark astounds us.
When we adopted Loki she was found in Indiana and scheduled to be put down. She was at the Huntley rescue for 2 days, enough time to get her spayed and that was all. Nothing was known about her except she was so damned cute and lovable.
We quickly found out she had a broken pelvis, which was either a car or an abusive person. We are guessing abuse because of the way she reacts when we leave the house. We think it's possible she was badly abused and then dumped onto the streets.
Getting her treated for the broken pelvis was very expensive and then we had to treat her for worms, she was infested with them. The first few months were difficult and I still have to watch the tone of my voice because if I raise it, just a little she becomes instantly skittish, which is so strange coming from such a self confident dog.
She litterly can go skittish in an instant, once my wife went to walk her when we were out traveling in our motorhome and Loki lost it, she started flopping on her back and looked to be convulsing but it was a panic attack. My wife gave her a sedative and she was fine after that. We took her to the Vet to see if it might be something more serious and he couldn't find anything wrong after testing for everything.
It's almost as if the dog was bi-polar, 99% of the time she is fantastic. Easily house broken, she never has accidents. She mostly listens, it's just this thing with the house that has us stumped. We are looking at local facilities that we can take her to that specialize in this sort of thing but they are costly and don't have openings until the Fall.