using the fact that current and motor torque have a linear relationship.
For a given position of the rotor, they do. However, what that relationship is will vary depending on the position. (Try turning a motor slowly - you will feel the torque changing significantly as coils come in and out of the circuit and the alignment of the coils relative to the magnets change.) If you want to apply a specific force, rather than apply a constant (but unknown) force, then I think you will need to provide a better way of determining the actual force and use a feedback algorithm to control it.