what are the forces that do cause the deflection we see,
Oh boy, this is getting tedious. It is called lift.
You admit that the R22 does not behave in the manner a gyroscope is obliged to perform. It has forces acting upon it. So it is only LIKE a gyroscope, which is the basic premise of the statements by Nick Lappos et al. It is not a straightforward gyroscope. It is LIKE a gyro.