I have the large Ortlieb saddlebag, and I can imagine there are a number of seats that bag wouldn't fit under. I had to mess around for quite a while before it fit on my saddle, and I would say my saddle is not at all unusual. The good news is that I now can carry a small watermelon or a severed head under my seat. You never know when that could come in handy

I don't know if you've used the bag, but twist the straps in the opposite direction from each other so they don't unwind. I don't know how Ortlieb gets the straps to look so flat in their pictures, I think it's misleading.