Makes total sense and I've found the same thing - people like a human element. And, animal stories are always a great route to go - few things showcase a better side of humanity than helping animals, and it's even better when you have a strong community tie to it.
For any project to be effective, things have to tie together, right? It needs to make sense to the audience. Human interest angles (an interview with the GM/profile of the GM) is a great starting point to bring in her love of animals and tie to the company, without the company or product being the focal point. And, to your point, it's can be used for FB content/social. The campaign can stem from that with the CTA of her helping to drive and encourage others to help animals (like the points you made about # of likes = sponsorship).
That can be the foundation, then shift towards the outcomes: what animals are sponsored, what their needs are, etc. You can do it in waves: establishing the connection between your company and animals, profiling your GM, shifting the focus to how the sponsorship of the animal is making a difference, how to drive the audience to get involved.
While slightly self-serving, is there a way to maybe leverage a patch into your project? I realize this could be asking a lot, but to tie it close with the company and what you do, I'm throwing it out there: a special patch that's part of the relationship with the Animal Sanctuary? Maybe with their logo? It could start as maybe a graphic design logo to use in any postings and such, then if there's a way, it could be manufactured with proceeds going to the sanctuary.
You can also do votes/polls = what animals to sponsor? Animal/sanctuary fun facts - easy sound bites for social media dissemination.
Again, it goes back to trying to make it less passive - how can people be part of something vs just reading about it or clicking a button.