The scheme recently proposed in [M. Scala et al., Phys Rev Lett 111, 180403 (2013)], where a
gravity-dependent phase shift is induced on the spin of a nitrogen-vacancy (NV) center in a trapped
nanodiamond by the interaction between its magnetic moment and the quantized motion of the
particle, provides a way to detect spatial quantum superpositions by means of spin measurements
only. Here, the effect of unwanted coupling with other motional degrees of freedom is considered and
we show that it does not affect the validity of the scheme. Both this coupling and the additional
error source due to misalignment between the quantization axis of the NV center spin and the
trapping axis are shown not to change the qualitative behavior of the system, so that a proof-ofprinciple
experiment can be neatly performed. Our analysis, which shows that the scheme retains
the important features of not requiring ground state cooling and of being resistant to thermal
fluctuations, can be useful for the several schemes which have been proposed recently for testing
macroscopic superpositions in trapped microsystems.