To be honest... my dogs picked me.

Simba gets along best with puppies. He doesn't care for them at first, but then (as you can see by the pics with Ki and Sim) he warms up to them.

I suggest just going to the shelter every once in a while. I'm not sure about there, but there's always tons of Pitties, GSD's and mixes of those breeds in our shelter.
I think you'd know what's best for Max and for your family once you go to the shelter.

To me, it sounds like what would be best for Max, a younger female.. of his size, or around there. Who's submissive yet is able to hold his/her ground (unlike the Chi's) and play with Max.

Fostering is a great idea. That way you can see how he'd react with another dog living in your home AND you'd be able to help the dogs at the shelter. And, you'd see how each dog would react to the chickens, cats, etc..