PnP transport
I use a collapsible, soft-sided medium crate. I remove the stick, seat cushion, and seat back. The crate sticks about 12" into the baggage area. The key is that the crate opens on the top rather than the front and I lower the animal in, rather than try to load a hard crate. My limit is 45#, primarily for the dog's comfort. This has worked well for me in over 100 transports. I'm not sure how well tethering a dog in a tandem aircraft would work. (I once had a dog manage to open the zipper. Luckily, she only wanted to look around. Gave me a start when she nudged my neck with her cold nose.) You'll no doubt find animal rescue one of the most satisfying uses for you plane.
Good luck!