But the results were unreliable, something along the lines of:
Press Power -> Laptop Suspends
Press Power -> Laptop Resumes, briefly, then Shuts Down
Press Power -> Laptop boots
I looked at the /etc/acpi/powerbtn.sh
I don't know how this script works but the last two lines caught my eye:
# If all else failed, just initiate a plain shutdown.
/sbin/shutdown -h now "Power button pressed"
Which makes it quite difficult to catch problems. So I commented out the last line:
sudo pluma /etc/acpi/powerbtn.sh
# If all else failed, just initiate a plain shutdown.
#/sbin/shutdown -h now "Power button pressed"
And that was sufficient to give me the result I was looking for. Now the power button consistently follows the actions in the Power Management settings.