Subject: Why don't gyrocopters stall?

Ok I've got a ridiculously detailed question on gyrocopters, that's been
bothering me for a while.

When a gyrocopter travels through the air, the leading wing will travel
faster relative to the air, hence will have more lift. The trailing edge
will travel slower and will lose lift. Therefore you might naively expect
the aircraft to lean over. But that's too easy.

The rotor is a big gyroscope really. Pushing up on one side of a gyroscope
usually causes movement 90 degrees away.

Therefore I would expect the front of the plane of rotor to lift and cause
the aircraft to kind of 'stall'.

That doesn't appear to happen. How come? Is it just that the pilot pulls
back on the stick to compensate or something? Or does this happen, but it
just results in more lift/drag? What's really happening here? Am I missing
anything?

Re: Why don't gyrocopters stall?