In my own personal opinion, the only time I feel it is right to put an animal to sleep is if they are sick or in pain.
I do know that the shelter I volunteer with is a no-kill, but they have had to "let" an animal go because it was just not going to.............I don't even know how to word it.
They choose animals after testing to see if they are adoptable. Some seem fine during the testing but then prove the opposite.
I believe the right person is out there for every animal. Sometimes that person is not found in time.

I do hope you can find the right place for Ollie where he can be well taken care of for the rest of his days, months, years.

You are definitely doing the right thing, for your self and Ollie.

Hugs to you through this difficult time.