In the older days, Fjällräven offered a stuffsack that was open on both sides, where you put in your rolled sleeping mat, let it snap open and stuffed your sleeping bag into the open space within the mat. It was meant to work with their external frame packs, in case of rain covered with the rain cover of the rucksack. It was about 30 cm diameter and 50 to 55 cm wide, without the closures. I had one made once by my wife, but the snapping open of the mat never happened due to the sticky material of the mat (Evazote), the option with putting the mat into the rucksack and putting the other gear inside the roll was always awkward due to the same reason.
Since then I changed to using TaR mats and never looked back, packing them flat along the back of my Duluth Packs as cushioning or packing them in their small packsack (not so much fun, I admit...).
I would go for a waterproof stuffsack and put some spare clothing or a small sleeping bag inside and everything outside the rucksack if you insist to do it this way...
Kind regards,
Heinz