'Torque motors' are rather different than most electric motors. They are specifically designed to be used at low or zero speed, and to maintain torque at zero speed (locked rotor) for indefinite periods of time.
They are essentially designed for locked rotor application.
As I recall, article 430 specifically mentions torque motors, and has specific requirements for their protection.
Don't think of this as 'going beyond code requirements for a normal motor'. Crack the book and follow the requirements for torque motors.
Depending on the specific design of the torque motor, you might get much better efficiency using a VFD, but this becomes a significant engineering project for what is probably a small motor designed to be used at 60Hz.
Edited to add: I see that 'torque motors' were not mentioned in the original post, but rather by the original poster later in the thread. My comments were directed to the use of motors designed for locked application, not ordinary motors that get locked up.