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It might be simpler to make a high precision current source, rather than measure the current. You could be using the same voltage reference for DAC,ADC and current reference. The instrumentation amplifier shall have all resistors with ultra low TCR.

EDIT:

Version 2. More complex, but AC:

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You do use a transformer and triac phase control. At very low conducting angle we cold say:

$$sin \ \omega t\approx tan\ \omega t \approx \omega t$$

Therefore

$$V_{SMA}sin \ \omega t\approx  V_{SMA} \omega t$$
$$R_{SMA}=\dfrac{\Delta V_{SMA}}{\Delta I_{SMA}} = \dfrac{V_{SMA} \omega (T_1-T_2)}{I_{SMA} \omega (T_3-T_4)}$$