= Solution
For $q=2$, at conjunction
$$
\phi=2(\lambda_c-\Omega_2).
$$
The stable geometry puts conjunctions a quarter orbit from either node, where $M_2$ has maximum vertical separation from the inner body's plane and close approaches are avoided. Therefore $\lambda_c-\Omega_2=\pi/2$ or $3\pi/2$, and both possibilities give
$$
\boxed{\phi\ \hbox{librating about}\ \pi\pmod{2\pi}}.
$$
This is <resonance protection>: the resonant phase moves conjunctions away from the two node crossings, where the physical separation would be smallest.
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