Are you sure about the seat size? I mean, I am much bigger than you, yet, a 16 inch, or 16.5 is best for me. It's not just whether or not one has "back" or not. It's also about the length of your femur bone.
I can't remember seeing a photo of you, but a 17 or 18 inch western saddle is one I would think a large man more suited for.