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 hole's 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 lump's 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. Comment: 10 pages, 7 figures
