You start out wonderfully with:
stuart0:
It's actually a lot simpler than that. Consider the 1st circuit with the diode.
Woo hoo! Looking forward to another explain-y thing which will help. ...er, and then:
stuart0:
Note that for any current to flow through the diode (D12) that it must be forward biased, but any forward bias on the diode reverse biases the transistor (Q11).
Uh oh.
stuart0:
Look closely at the circuit,
(Exactly how cross-eyed do you want me to get?)
stuart0:
the BE junction of Q11 and the diode are in "anti-parallel" configuration (in parallel but pointing opposite directions).
"anti-parallel"? "pointing [in] opposite directions"? Huh? Not from what I can see. You have now completely messed up everything I thought was happening there; I liked my explanation better.
You did say "It's actually a lot simpler than that" - which seems to imply that perhaps my explanation (though maybe using unconventional terminology) was reasonably accurate? ...at least in consequences?
stuart0:
It's very much the same situation in the second circuit. The BE junctions of Q21 ans Q22 are also anti-parallel, so when Q22 is conducting then Q21 MUST be off and vice versa.
Pray tell; what is this "anti-parallel" of which you speak, my good sir? 
Alright. On to some of your other responses.
First, thank you for clarifying the "resistor in series with a MOSFET gate". As for a specific circuit to which NOSUM's comments applied, it was definitely the totem pole circuits I was proposing. Your comment about not combining a resistor before either totem pole element and a resistor before the gate makes sense. (I'm looking forward to NOSUM corroborating this.)
stuart0:
Nothing wrong there with the basic circuit. Just remember to add the gate zener and some power supply bypass capacitors as close as possible to the switching device.
Glad I got that right, and yep; already being considered.
stuart0:
Also, you may need to check how much inductive energy there is when you come to switching (off) the actual halogen globes (including wiring inductance between your circuit and the lamps). You may eventually need some form of snubber or a catch diode there if the voltage overshoot is too much.
I've thought about this, and will be exploring this in more detail when I get that far. (As is likely apparent, this may be a while yet. :
) Quick question: could such a snubber or catch diode occur close to this circuit vs close to the actual load?
Thank you for your patience and continued participation, Stuart.
PS For those who may have lost sight of the original goal of this project, this topic deals with just the "driving the PMOSFETs part" of my goal to replace the turn signal flasher unit in my 2014 Scion FR-S with a fully programmable one. I know: "WTF?" Well, that's only the beginning. Turn signals do not need 10A-capable switching circuits, but the ability to programmatically control various lights for cars leading parades or at car shows does. 8) Plus, this wouldn't be fun unless it was at least perceived to be - at best - unnecessary. 
Cheers!
Dirk