(Please note ... we are not in disagreement, but I wanted to address this)

Asking how 'planes fly upside-down and putting one's theory to the test in this thought experiment is useful, but it doesn't refute the "downwash" theory. If you have a wing at an appropriate angle of attack, even if upside-down, then provided the flow remains attached, it (the flow) can still be deflected downwards.

If the wing is reasonably asymmetrical then the angle of attack needs to be large, which makes it more likely that the flow will become detached, so we deduce that a 'plane designed to fly upside-down needs to have symmetrical, or near symmetrical, aerofoil profiles ... which they do.

So the downwash theory is not refuted by the "upside-down" question.

(Please note: All that notwithstanding, the unadorned downwash theory is not the complete explanation of how lift is generated)

They don't do so at the same angle of attack I'd wager. Meaning to fly upside down they have to control pitch in a way that turns the wing to the exact needed angle. Same way they have to control pitch when flying normally to achieve lift.

This pic of real jets doing that side by side confirms what I'm saying (nose is pitched up on the normal-flying plane and 'down' but still up relative to the ground on the inverted one): https://imgur.com/loVcrgO

Great question, but the physics is still the same. The aircraft still generates lift by direction air in a downwards direction. For some aircrafts (based on the wing geometry), you can achieve this upside down, within a certain range of angle-of-attack of the wing. Obviously, the aerodynamic efficiency is not the same. Airfoil sections are anti-symmetric across this direction because these designs achieve higher L/D (lift to drag) ratios.