Boy, I'm good at messing up transistors!  This time it was just the pin
numbers for the collector and emitter reversed, because I didn't copy
the symbol from the datasheet but rather assumed another SMT 2222 would
have the same pinout.  Interestingly, it actually was able to control
the MOSFET at VBUS = 5 V and at VBUS = 9 V, but at VBUS = 15 V the
reversed transistor couldn't pull the MOSFET gate down enough.

I had the source and drain reversed—whoops.  After fixing it with an
X-Acto knife and some point-to-point wiring, I've updated the schematic
and PCB files accordingly.

THIS ALSO MARKS THE BEGINNING OF DEVELOPMENT OF THE NEXT BOARD REVISION.

Tested to probably not blow anything up if assembled properly!