Okay, why not just make followers out of animals, and let them breed faster than humans?
1) Without access to human souls, the populace will produce more demon-possessed people.
2) They'll want to worship a deity born of their species.
3) Once they provide more than half the faith, THEY become the dominant worshippers, and begin rewriting your Primary and Secondary domains to suit their religious needs.
4) Civil War between the 'true' people and the human populace.
5) Fate might take notice of all those souls springing into a rapidly growing race.
6) Take a look at Watership Down; bunnies compete for resources. Other animals will have their own ways of doing so.
7) As the animals destroy the ecology around them, the humans will have no food source except the animals.
The strain the young ones put on society leads to abominable mortality rates, leading to a crisis of faith - or enough miracles to make the new race Dependant.
9) The animals divide themselves into tribes, each requiring its own set of upkeep miracles.
Kargore loves you, and moves his worshippers in to enjoy the hunt.
There must be some reason why the Elder Gods haven't done this, and why human deities don't. The point of this thread is to point out disadvantages of 'Uplifting' animals to worshipping ability. Feel free to start another thread if you want to discuss another aspect of this issue.