"Creating God in our image"
I would only only only put a dog to sleep because I did not have the ability to heal it and make things right.
God has the ability to heal ALL because he is infinite.
Man has made the very dire mistake of making God finite.
"Putting them out of their misery" doesn't work with an infinite being. You have convinced yourself of this but you will realize that this is the very wrong assumption.
That is pure rationalization.
The problem is that we HAVE to rationalize and you can't be rational about the infinite.
We simply cannot understand infinite mercy, infinite grace, infinite love, and infinite justice. Because of this we explain God in our terms - finite terms. We limit God because we are limited.
Did God create us in His image, or did we "create" God in our image?