The first prototype has begun testing. The first thing that was discovered was that the BSS84 is not a good choice for the power gating transistor at 3.3 volts. The power output on the drain was closer to 2 volts, and was insufficient to allow the module to power up. Replacing the transistor with a wire from source to drain fixed the problem, albeit without being compliant with the USB spec.
The best case scenario is simply swapping out for a better transistor solving the problem. At the moment, the candidate is the SI2329DS-T1-GE3. It has a lower Vgs to Rds-on resistance curve, making it more likely to pass sufficient current when Vgs is only 3.3 volts.
EDIT: The FDV304P is also a good choice, and I’ve confirmed it works.