So if the force on the nozzle is drag, how does it increase the thrust?
I think where Keith is going is to look at
you integrate the pressure over the internal space
A common presentation is to look at the pressure forces throughout the engine. Especially for the FJ folk, a lot of the net thrust comes from careful and clever intake design (the airflow has to be slowed down to subsonic flow at the engine intake face) and then there are bits and pieces throughout the engine where local net forces are forward or aft.
The bit coming out the back is only part of the equation ...