Welcome back, I'm so sorry that your post since last time has to be an update like this.
There could always be a chance that she can find her way back. Did you have her favorite treats offered outside - I'm not sure about the pests around there, but it's a starting to getting your bird back.
The eating part seems to be the most worrisome. A mirror, TEMPORARILY could be an option for now to substitute the loss of his mate. I'm sorry, but I can't help you that much with the eating and his depression so hopefully someone who was able to deal with this can chip in.
Just if your'e wondering about adding another bird: Parrots are able to tell other parrots apart, your next Ringneck could be identical yet Michael will know the difference and theres a risk of them not getting along and being aggressive. If you do decided on another bird, please take the process of introduction slow if there's any signs of distress from either one (Don't forget the quarantine!).