Ah, actually we did interpret that walkers could hop directly from flatdog to flatdog, but the rules seem clear that you can't on second glance. I'm not sure if that addition would change things much, but it made one of our games very dramatic!
After testing it a bit, being able to jump between the dogs seemed like at least it wouldn't cause problems, so I'll update the rules to allow it. Thank you very much for the feedback! :)