Peter, - "A barrel roll is not really flying upside down, BUT

With sufficient thrust, airframe strength, pilot skill, not too inappropriate wing sections, and the appropriate angle of attack, some aircraft can fly upside down, steady state, but usually not nearly so well as the right way up."

Any airplane can fly upside down, the problem is the fuel pickup and oil pickup in the engine.  Aerobatic planes solve it with a fuel header tank and and an oil pickup in the heads.  Symmetrical wings on airplanes are common especially for the tail feathers.

By the way, I would bet that I have over 10 hours of inverted flight, or at least semi inverted.

You are kind of right, Barrel rolls and zero G maneuvers, don't have a preference for facing the earth.  It is really, really easy to get confused and not know which way is down.

Talador