I was only agreeing with you and I thought tidying up a bit
but my son has made a similar point from time to time.
So for the O/P,
The part I am struggling to grasp is ....,
"Since heat does not leave the affected air mass, this is an adiabatic change of pressure, with an associated change of temperature."
??Heat does not leave...but there is an associated change of temp???
In this case the starting point I guess had probably to start with the relationship and meaning of energy/work/heat and how you cannot talk about the quantity of heat or work in a substance but you can talk about energy.
Compress a gas in an insulated container and it will increase in temperature on account of the work done on it. Repeatedly bend a paper clip till it breaks and it will be much hotter than its surroundings etc. All work to me.
So
a) energy can enter a substance without flow of heat (by 'working it')
b) adiabatic means no more than insulated to prevent heat flow
c) so if the 'adiabatic change in pressure' was a compression then work was done on the gas (eg by something pushing a piston against the resisting pressure) and it will get hotter: if the gas expands and looses pressure it will cool -it's done work by pushing other stuff out of the way to claim the extra space.
I thought that did it..........or have I lost track ?