Nick and Q,
I have just read both of your posts a couple of times and with the exception of a couple of points in Q's last post I think you are both arguing the same point. Nick is taking the standard mathematical approach in flight mechanics of referring the forces and moments back to the aircraft CG while Q is using the hub.
When balancing forces you balance in the three directions and the line of action of forces is very important (i.e its point of application). The point of application of a moment on a body is irrelevant as long as the axis about which is occurs is known. Therefore, whether you choose to take moments and do the force balance about the hub or the CG the answer will be the same. Provided you stick to your convention and consider all of the forces.
Taking moments about the CG (as Nick has) means that weight cannot provide a moment as there is no moment arm. MR side-force and TR thrust both produce moments about the CG and hence the perpendicular distance is important.
Taking moments about the hub (as Q has) means that the MR side force cannot provide a moment as again their is no moment arm. However, the tail rotor thrust provides a moment as does the weight, so in this case it is the perpendicular distance of the TR thrust from the hub and the CG from the hub that is important.
If you adopt either system and follow either convention through thoroughly then they will both give the right answer. It is common to take moments through the CG since is simplifies the maths significantly as we are fundamentally dealing with inertial forces in aircraft. The acceleration due to gravity (9.81 m/s/s) and any additional maneuver accelerations.
Fundamentally, Q, the height of the MR and TR from the CG are important even in steady state hover because the weight and inertial forces can be idealised as acting at the CG, but your view of taking moments about the hub is correct providing you follow the same convention all the way through your analysis.
I also agree that in a teeter-rotor helicopter with the TR hub at the same height as the MR in a perfectly trimmed helicopter with no other external forces acting on it (CG directly below hub centre) then the helicopter would hover skids level. However, this is because both FORCES, (TR Thrust & MR Side force) are equal and opposite and have the same moment arm about the CG.
Hope this helps
CRAN
