I am so sorry, and my heart goes out to you. This is so hard, I know. We have loved them so much but circumstances got in the way, or something happened. The vet could be right, that aggression could have been genetic. In which case there was nothing you could do. To keep Elvis going could have made things worse daily, until he had no peace of mind at all, and was constantly in a state of fear-aggression. That is a terrible situation to be in for a dog. Constant stress and no peace. At least this way he has some peace now.
It is so sad. I wish I could give you a hug. And I feel sorry about Elvis too.
Do send him your love. He will sense it and it could help him. But he will be in a much better state now he is in spirit.