I think it will definitely be slouchier at the bottom than your LV, but once you start filling it, it has nowhere to go but out! I felt the east/west kind of protruded too once I put things in it which is another reason I tried to carry very little - kind of like wearing a too-small shirt so your arms start sticking out!! Perhaps if the north/south hangs lower than the east/west, where it sticks out will be less bothersome?
(Edit: add: Hopefully someone will come along who has this actual bag. I've heard others mention they liked wearing the n/s shape better than the current e/w, so I think there are a few owners!)