In this paper we continue the first ever study of magnetized mini-disks coupled to circumbinary accretion in a supermassive binary black hole (SMBBH) approaching merger reported in Bowen et al. 2018. We extend this simulation from 3 to 12 binary orbital periods. We find that relativistic SMBBH accretion acts as a resonant cavity, where quasi-periodic oscillations tied to the the frequency at which the black holes orbital phase matches a non-linear $m=1$ density feature, or ``lump, in the circumbinary accretion disk permeate the system. The rate of mass accretion onto each of the mini-disks around the black holes is modulated at the beat frequency between the binary frequency and the lumps mean orbital frequency, i.e., $Omega_{rm beat} = Omega_{rm bin} - bar{Omega}_{rm lump}$, while the total mass accretion rate of this equal-mass binary is modulated at two different frequencies, $gtrsim bar{Omega}_{rm lump}$ and $approx 2 Omega_{rm beat}$. The instantaneous rotation rate of the lump itself is also modulated at two frequencies close to the modulation frequencies of the total accretion rate, $bar{Omega}_{rm lump}$ and $2 Omega_{rm beat}$. Because of the compact nature of the mini-disks in SMBBHs approaching merger, the inflow times within the mini-disks are comparable to the period on which their mass-supply varies, so that their masses---and the accretion rates they supply to their black holes---are strongly modulated at the same frequency. In essence, the azimuthal symmetry of the circumbinary disk is broken by the dynamics of orbits near a binary, and this $m=1$ asymmetry then drives quasi-periodic variation throughout the system, including both accretion and disk-feeding. In SMBBHs approaching merger, such time variability could introduce distinctive, increasingly rapid, fluctuations in their electromagnetic emission.
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