It's so great that you want to change things for the better and oust a bad manager. Probably a dumb question, but have you tried passing out fliers outlining all the horrid things done there? Places like Petsmart might be willing to help distribute fliers, as would any local rescue group. If there's anything like an Adoption Option where rescue groups congregate to adopt out pets, make them aware of the situation and I bet most would be willing to help distribute fliers.

While the more people you can get to sign the petition and write in to the board of directors will have some impact, what you really need is a strong local outcry. The more people in that shelter's area who say, "We're not going to stand for this!" the more likely you probably would be to see a change in that area. At least, that seems like the way it should work.