Hello, I'm Dr. Deb and will do my best to help you today.
I'm so sorry that you lost Parker in this way:( You must still be absolutely bereft although I hope you can find comfort knowing that he passed at home under his favorite tree.
Considering how bonded he and Loki were, it's not uncommon for the friend left behind to mourn and grieve as Loki is doing. This process is quite variable among dogs: it can take just a short time before they seem to move on or it could last for months.
When faced with similar situations with my owners, I often suggest that they consider getting another dog sooner rather than later. A puppy is often a good choice since they take rejection fairly well (which may be Loki's attitude at least initially) and are such a joy to have around.
A puppy may be just the thing to take Loki's mind off of Parker or at least help him to get past his grieving. They may help not only Loki but also you and your husband during this grieving process.
A young adult may also be a possibility since he/she will have an established personality but obviously, Loki would have to "approve" of them which may be hard for him to do in his current mental state.
I don't know if something like a DAP collar (or something similar) will be of benefit for him but it might be worth a try. These collars contain natural pheromones which are intended to reduce anxiety and instill a sense of calm. They don't work for every patient but they aren't harmful.
Here in the States, they're available at local pet/grain stores or can be purchased online.
Again, please accept my sincere condolences on your loss; I know there's going to be a big hole in your hearts for a long time to come.