I doubt anyone can make a convincing argument about how your ideas of a compost pile should be.
With such unusual add-ins, it doesn't make sense for anybody to try to change your mind.

Dog and cat feces, birds, cats, rodents.....mmmmm gooood.

Well, each to his or her own.

Well, people say that you can use UCG's straight to their final resting place, no composting necessary.

I'm sure that if you had a pile of 70% UCG and paper filters, then you would soon have a pile of 69% UCG, and 1% decomposed UCG/filters. Over more time you'd have just decomposed UCGs. Is that compost...I'm sure you could argue it's a _type_ of compost, maybe not the most balanced, but still useful!

If I had that much, I'd spread the UCGs over my lawn, then put the remainder (and filters) and put in in my pile. But as jeannie7 said: "each to his or her own"

HOW you use it aside, unless you're talkin' truckloads of UCGs, I don't think you can go "too much." There's so much in one's landscape that you can use it for before you need to start worrying about chemistry.

Coffee grounds are relatively high in nitrogen, so you might get some smell if you have too many of them in the mix, especially since it sounds like you're using a fair amount of other ingredients that are high N (like the animal waste and dead animals for example).

You might want to add enough coffee grounds to heat the pile a bit, but if it starts to get to be too many, you can fling them around the lawn, where they'll act as a mild fertilizer and an amendment. If you do that, you don't want to get them more than about 1/4 inch thick because they can repel water when they're too thick.