I know a lot of people don't like to go upside down but you have nothing to worry about on the shoulder harnesses/lap bars as even if they were not there you would still stay in your seat due to gravity. When you go through any inversion (track that takes you upside down) gravity pushes you down, you experience positive G-Forces, or gravitational forces.
Actually the first coaster to have a loop (Revolution at Six Flags Magic Mountain) did not have horse collars (think Rockin Roller Coaster) but had a lap bar, they have changed it since then, but many coasters built by the same company still have lap bars and I personally feel are much better due to that fact.
BTW Expedition Everest does NOT go upside down, but it does go backwards and forwards.
Jennifer