When you do this problem, don't miss the opportunity to compare it to the
problem of the particle sliding down an inclined plane. Prima facie, the
student may think that the pendulum problem is only an inclined plane
problem with a varying slope angle. Of course he needs to learn that the
rigid inclined plane forces the transverse acceleration to be zero, while
the curved path of the pendulum requires a velocity dependent centripetal
acceleration.
Also add a comparison to the banked curve problem, where the desired
centripetal acceleration is horizontal.
P.S. Michael, your treatment admits a second solution: T=0!