On an energy-maneuverability (E-M) diagram how does the shape of a specific excess power (Ps) curve change as thrust is increased or decreased?
The shape does not change much, but they shift up and down. Below you see a diagram I once made for a HALE unmanned airplane with a turbofan engine. Instead of varying thrust I calculated the instationary turn rate at different sink speeds. Sinking frees up energy similar to a thrust increase, so these curves should look the same for different thrust levels. After all, the unit for SEP is a speed, too.

Turn rate diagram for different sink speeds and flap settings. Blue lines are for cruise and red curves for the landing setting of a simple camber flap. The aerodynamic model did not include wave drag, so the results above Mach 0.7 are not correct.
As you rightly assumed, the curves shift to lower speeds for lower thrust, but only the red ones become flatter for lower sink speeds / thrust levels.