We explore the influence of nongeodesic pressure forces present in an accretion disc on the frequencies of its axisymmetric and nonaxisymmetric epicyclic oscillation modes. We discuss its implications for models of high-frequency quasi-periodic oscillations (QPOs), which have been observed in the X-ray flux of accreting black holes (BHs) in the three Galactic microquasars, GRS 1915+105, GRO J1655−40, and XTE J1550−564. We focus on previously considered QPO models that deal with low-azimuthal-number epicyclic modes, |m| ≤ 2, and outline the consequences for the estimations of BH spin, a ∈ [0, 1]. For four out of six examined models, we find only small, rather insignificant changes compared to the geodesic case. For the other two models, on the other hand, there is a significant increase of the estimated upper limit on the spin. Regarding the falsifiability of the QPO models, we find that one particular model from the examined set is incompatible with the data. If the spectral spin estimates for the microquasars that point to a >  0.65 were fully confirmed, two more QPO models would be ruled out. Moreover, if two very different values of the spin, such as a ≈ 0.65 in GRO J1655−40 and a ≈ 1 in GRS 1915+105, were confirmed, all the models except one would remain unsupported by our results. Finally, we discuss the implications for a model that was recently proposed in the context of neutron star (NS) QPOs as a disc-oscillation-based modification of the relativistic precession model. This model provides overall better fits of the NS data and predicts more realistic values of the NS mass compared to the relativistic precession model. We conclude that it also implies a significantly higher upper limit on the microquasar’s BH spin (a ∼ 0.75 vs. a ∼ 0.55).Key words: X-rays: binaries / black hole physics / accretion, accretion disks