OK Shawn, back to even more basics, lets leave aside any rotor efficiencies and just look at the power output from the engine's N2 shaft where T5 is limited. I maintain that there isn't constant power available regardless of N2 rpm - in a "reductio ab absurdum", taking the N2 towards zero, the torque would not tend towards infinite (even assuming there is no surging etc), so clearly there is an optimum N2 where power from the engine is maximised for a given limiting TOT. My gut feeling is that the power would be greater at higher N2 rpm, since fuel flow could be increased for a given T5 (because of greater air flow). The limiting factor may be the stresses and structural integrity of the N2 turbine wheel and / or the way the turbine guide vanes are tuned.
But not an engine thermodynamic expert so don't shoot!
HC