Let's say the engine is mounted such that it is acting through the CoM,
OK? In that case, changes in thrust cannot *possibly* cause any net
torque, right?

Yep. Drag is not at the center of mass

OK, move the engine up or down, and if you reangle it to set the thrust
line through the CoM, then the same situation holds true.

Nope. Drag is not at the CoM
--
Jim in NC