Information update:
The zeners in series work. Since I already got 16v zeners, I'll add a 3.3v zener for the +12 lines, limiting the driver output to 19.3v, and giving me a max Vgs of 7.3v .
From the datasheet of the 1163 driver, it's suggested to add a 150 ohm resistor to the supply pin, if negative transients are expected. 300 ohm is recommended for the 1154 driver.
From IRF:
Gate Drive Characteristics and Requirements for HEXFET® power MOSFETs (PDF, 21 pages)
There are a number of ways suggested to drive the gate of a MOSFET.
IRL have a min Vgs of 1 to 2v, instead of the IRF's 2 to 4, to turn on the MOSFET.
The Do's and Don'ts of Using MOS-Gated Transistors (PDF, 7 pages)
From that, I can see that my suggestion to reverse the Source and Drain, would actually allow the PSU voltage to get to the power bus, with a certain voltage drop, regardless of the state at the gate. Back to the sketchboard.
I can also see the detail of the purpose of the zener: the transient to the gate comes from voltage drops at the source/drain.
Note to self, for the next time I do this: consider IRF2804 or IRFP2907, or a good IRL.