The "Extended Orbital Resonance Model," i.e., the idea of oscillations induced by the hump of the orbital velocity profile (related to the locally non-rotating frames - LNRF), which are proposed to excite the oscillations of Keplerian discs around near-extreme Kerr black holes with epicyclic frequencies, is used to estimate the mass and spin of three near-extreme Kerr black hole candidates GRS 1915+105, XTE J1650-500, and NGC 5408 X-1. The hump-induced oscillations are characterized by the so-called "humpy frequency," and a non-linear resonant coupling between these and epicyclic oscillations is expected. It it shown that the quasiperiodic variability (QPOs) observed in these sources can be matched with the proposals of the model, giving for the mass and spin of their black holes values consistent with the other observationally-established estimates.