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Recent radiation-thermochemical-magnetohydrodynamic simulations resolved formation of quasar accretion disks from cosmological scales down to ~300 gravitational radii $R_g$, arguing they were ‘hyper-magnetized’ (plasma $\beta \ll 1$supported by toroidal magnetic fields) and distinct from traditional $\alpha$-disks. We extend these, refining to $\approx 3R_g$around a BH with multi-channel radiation and thermochemistry, and exploring a factor of 1000 range of accretion rates ( $\dot{m}\sim 0.01-20$). At smaller scales, we see the disks maintain steady accretion, thermalize and self-ionize, and radiation pressure grows in importance, but large deviations from local thermodynamic equilibrium and single-phase equations of state are always present. Trans-Alfvenic and highly-supersonic turbulence persists in all cases, and leads to efficient vertical mixing, so radiation pressure saturates at levels comparable to fluctuating magnetic and turbulent pressures even for $\dot{m}\gg 1$. The disks also become radiatively inefficient in the inner regions at high $\dot{m}$. The midplane magnetic field remains primarily toroidal at large radii, but at super-Eddington $\dot{m}$we see occasional transitions to a poloidal-field dominated state associated with outflows and flares. Large-scale magnetocentrifugal and continuum radiation-pressure-driven outflows are weak at $\dot{m}<1$, but can be strong at $\dot{m}\gtrsim 1$. In all cases there is a scattering photosphere above the disk extending to $\gtrsim 1000R_g$at large $\dot{m}$, and the disk is thick and flared owing to magnetic support (with $H/R$nearly independent of $\dot{m}$), so the outer disk is strongly illuminated by the inner disk and most of the inner disk continuum scatters or is reprocessed at larger scales, giving apparent emission region sizes as large as .