The good news is that you have tons of options.
First, go canned. That'll help with the weight problem.
Nature's Variety, Natural Balance, and Evo come to mind as foods that offer what are called novel protein sources. In other words, unusual meats.
Nature's Variety Instincts (canned food) offers beef, rabbit, lamb, duck and venison. I believe their Prairie line of canned foods also has a good variety of protein sources.
Natural Balance has a venison & green pea canned food that is reasonably priced and is pretty decent.