We present Stratospheric Observatory For Infrared Astronomy (SOFIA) + Atacama Large Millimeter/submillimeter Array (ALMA) continuum and spectral-line polarization data on the massive molecular cloud BYF 73, revealing important details about the magnetic field morphology, gas structures, and energetics in this unusual massive star formation laboratory. The 154 mu m HAWC+ polarization map finds a highly organized magnetic field in the densest, inner 0.55 x 0.40 pc portion of the cloud, compared to an unremarkable morphology in the cloud's outer layers. The 3 mm continuum ALMA polarization data reveal several more structures in the inner domain, including a parsec-long, similar to 500 M (circle dot) "Streamer" around the central massive protostellar object MIR 2, with magnetic fields mostly parallel to the east-west Streamer but oriented north-south across MIR 2. The magnetic field orientation changes from mostly parallel to the column density structures to mostly perpendicular, at thresholds N (crit) = 6.6 x 10(26) m(-2), n (crit) = 2.5 x 10(11) m(-3), and B (crit) = 42 +/- 7 nT. ALMA also mapped Goldreich-Kylafis polarization in (CO)-C-12 across the cloud, which traces, in both total intensity and polarized flux, a powerful bipolar outflow from MIR 2 that interacts strongly with the Streamer. The magnetic field is also strongly aligned along the outflow direction; energetically, it may dominate the outflow near MIR 2, comprising rare evidence for a magnetocentrifugal origin to such outflows. A portion of the Streamer may be in Keplerian rotation around MIR 2, implying a gravitating mass 1350 +/- 50 M (circle dot) for the protostar+disk+envelope; alternatively, these kinematics can be explained by gas in free-fall toward a 950 +/- 35 M (circle dot) object. The high accretion rate onto MIR 2 apparently occurs through the Streamer/disk, and could account for similar to 33% of MIR 2's total luminosity via gravitational energy release.