How to predict and compensate for the dynamic and static resistive torque due to losses in a motor
The simplest solution is to use a coreless or 'ironless' motor. With good bearings the drag at low speed should be be very low. Brushed coreless motors also have the advantage of very low inertia.

As an example of how free a coreless motor can be, the ironless brushless motor below can be used as a compass! The rotor spins so freely that - with no iron to cause cogging or eddy current drag - when unpowered it aligns itself to the Earth's magnetic field.  



The downside of coreless motors is higher resistance for the same Kv, since there is less or no iron to concentrate the magnetic force so more turns of wire are required. This means you may have to use a larger motor to get the power (torque x rpm) that you need.

Unfortunately high power low rpm brushed coreless motors are hard to come by these days. Ironless BLDC motors are more common, or you could try building one yourself.


  Ultimately this system will be used to modify the stiffness of a
  mechanical torsional spring without adding damping.


Motors are designed to rotate continuously, whereas springs have limited travel. For this application you might consider a different type of control such as a 'voice coil' actuator, or perhaps use the motor to drive some mechanism which adjusts the mechanical stiffness of the spring.