I guess your asking for something like, what is the minimum [tex]\omega_s[/tex] so that this precession will still occur?
I would go back to the 'droop' idea. As the angular velocity of the wheel decreases, the wheel will continually droop such that [tex]\vec{F_g} \times r[/tex] or in scalar form [tex]Mgr sin\theta[/tex] will be the torque [tex]\tau[/tex] to maintian the equation of gyration. The smallest possible value of theta would be such that the wheel is about to touch the center pivot. This will probably correspond to your minimum speed you are looking for.
