Thanks for all the advice, and your patience!
Looking through lots of datasheets I've found P-channel MOSFETs with negative threshold voltages. I understand these are enhancement mode fets and require a negative voltage to open the channel. Correct?
Unfortunately that's the only type I can seem to find!
One example is this one
Very low threshold voltage (-0.4 to -0.68)
Logic level compatible
I suspect I'm wrong about enhancement mode fets and that they are simply opened with a voltage difference, either from +5 to gnd or gnd to -5v.
I' also found some through-hole alternatives on rapid online
(though they've lower power rating):
ZVP2106A P CHANNEL MOSFET:
Gate source threshold voltage max -3.5V
So does that mean it will be opened by a voltage drop from +5V to +1.5V or lower (i.e. gnd)?
I guess I could always get some parts and experiment.