Estimations of black hole spin in the three Galactic microquasars GRS 1915+105 , GRO J1655-40 , and XTE J1550-564 have been carried out based on spectral and timing X-ray measurements and various theoretical concepts . Among others , a non-linear resonance between axisymmetric epicyclic oscillation modes of an accretion disc around a Kerr black hole has been considered as a model for the observed high-frequency quasi-periodic oscillations ( HF QPOs ) . Estimates of spin predicted by this model have been derived based on the geodesic approximation of the accreted fluid motion . Here we assume accretion flow described by the model of a pressure-supported torus and carry out related corrections to the mass-spin estimates . We find that for dimensionless black hole spin a \equiv cJ / GM ^ { 2 } \lesssim 0.9 , the resonant eigenfrequencies are very close to those calculated for the geodesic motion . Their values slightly grow with increasing torus thickness . These findings agree well with results of a previous study carried out in the pseudo-Newtonian approximation . The situation becomes different for a \gtrsim 0.9 , in which case the resonant eigenfrequencies rapidly decrease as the torus thickness increases . We conclude that the assumed non-geodesic effects shift the lower limit of the spin , implied for the three microquasars by the epicyclic model and independently measured masses , from a \sim 0.7 to a \sim 0.6 . Their consideration furthermore confirms compatibility of the model with the rapid spin of GRS 1915+105 and provides highly testable predictions of the QPO frequencies . Individual sources with a moderate spin ( a \lesssim 0.9 ) should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin ( a \sim 1 ) . This should be further examined using the large amount of high-resolution data expected to become available with the next generation of X-ray instruments , such as the proposed Large Observatory for X-ray Timing ( LOFT ) .