You could make a bungie cord system for the pack? Poke some holes at the corners and down the sides of the back piece. Then thread some bungie cord through it that will fit for the sleep pad?
or, after you've placed the pack on the dog, wrap some cord around both the sleep pad and your dog's stomach until it is secure. This would probably be uncomfortable for the dog and would be a pain to take on/off
Depending on how long that pad is and the size of the dog, would it hinder the pup's movement when he is jumping/running? At least my dog occasionally sticks her butt up in the air when she runs like a Deer…..but she is pretty odd…..