Sleeping bag goes on the inside. you wanna keep it dry and not lose it on the trail.

I keep mine at the bottom of my pack. it's the first thing I load into it at the very bottom.

Yes my sleeping bags are lighter and pack smaller than yours, but there's no reason why yours isn't perfectly useful given enough pack volume. You might want to look for an appropriate sized compression sack to crunch it down a little smaller, but there's no reason why it shouldn't be stuffable into the bottom of a backpack.

(mods, this thread does probably belong in beginners..)