If you're using a cheap synthetic bag, tying to the outside won't be as fatal as having a down bag outside. It'll still work with tears in the shell.

I use a 40 liter pack and have a down quilt and a NeoAir - both will go inside the pack, every time, so I can drop my pack on the ground without fear. Since they pack smaller than a Thermarest and sleeping bag I have plenty of room for the rest of my gear.

In the days when external frame packs were popular and you saw folks hiking along with bedrolls on the bottom, that was a usual thing - foam pads and big synthetic bags don't suffer as much as the inflatable pads and mattresses and down bags with very light shell material will.

If you want to use the gear you have and it won't fit in, the cure is a larger pack - maybe a 50 or 60 liter. 40 is usually considered an extended day pack.