I think measuring the motor current is not a bad idea.
I wouldn't use, however, a strong stepper motor directly but a weaker one in combination with a reduction gear.
That way you get many rotations at the motor axis even if the angle of torsion at the specimen is only very small. So the current measurement can be averaged over several turns.
I assume that accuracy will then be by far enough for your application (<<20%).
Also measuring the torsion angle will be much easier if done at the motor axis (before the reductio gear); e.g. using an incremental angle encoder, or, if a stepper motor is used, simply by counting the steps.