I don't know of any list, per se, and I really don't know much about this subject. You might start at
http://ech.cwru.edu/ech-cgi/article.pl?id=O3

It gives some of the history of orphanages in Cleveland, although it undoubtedly doesn't come close to naming them all. But it might give you some info to start googling with.

Wish I could help.
Linda