So, you want to use a servo? Why not just buy a servo?
Three things are required for "motor action" -
- A current carrying conductor
- A magnetic field
- An applied voltage
The result is relative motion between the conductor and the magnetic field.
Three things are also required for "generator action" -
1. A current carrying conductor
2. A magnetic field
3. Relative motion
The result is a voltage developed across the conductor.
This is important because once a motor starts it also becomes a generator of sorts, because it meets the criteria required for generator action.
The generator action in a motor will develop what is referred to as "back EMF". It is a voltage that acts against the applied voltage. The back EMF "fights" the applied voltage, which reduces the net voltage applied to the motor, which reduces the current draw.
The torque a motor can produce will always be directly related to the strength of the magnetic field inside the motor. The strength of the magnetic field is directly related to the current in the motor windings.
You make more torque in a motor by passing more current to the motor.
As you have noticed, more current leads to more heat in the motor, because of "I squared R losses." This term comes from the formula for electric power, $P = IV$, combined with Ohm's Law, $V = IR$, to give a formula for electric power in terms of current and resistance:
P = I^2 R \\
The $I^2R$ losses are the reason why high voltage electric lines are used for power transmission - higher voltages reduce current. Power losses increase with current squared, so it's important to get current as low as possible to reduce the power losses.
So, in order to get a high stall torque, you need a high applied current. As you have seen, you cannot take a "standard" or general purpose motor and use it at stall conditions because most motors are designed with back EMF in mind. The back EMF protects the motor by reducing current draw, which reduces the heat generated ($I^2R$ losses) inside the motor.
To operate predominately in the stall region of a motor requires more cooling to dissipate the heat generated, and/or different wire insulation that is capable of withstanding higher winding temperatures.
A motor spec sheet should list the "nominal" or operating current for the motor. The alternative to buying a specialized motor might be to operate the motor in conjunction with a current-regulated power supply instead of a voltage-regulated power supply. Throttle the motor to no more than the specified operating current and the heat generated in the motor should be manageable.
I say this might be acceptable because most higher-power motors feature an integrated fan. If the motor has a fan, then the rated current for the motor likely depends on the fan rotating at the nominal motor speed.
You can meet the requirement by creating a blower for the motor - this is a common practice where slow speed, high torque motors are used, as in cranes. Essentially, you disconnect the fan from the motor you want to operate at stall condition and attach it to the output shaft of a second motor. Any time you apply power to the first motor, you spin the second motor at whatever speed the fan is supposed to turn.
Now you get all the design cooling for the first motor and, assuming you're operating at or below the rated current for the first motor, you should be able to operate at or near stall torque for as long as you want.