A novel technique combining Brillouin phase-shift measurements with Brillouin dynamic gratings (BDGs) reflectometry in polarization-maintaining fibers is presented here for the first time. While a direct measurement of the optical phase in standard BDG setups is impractical due to non-local phase contributions, their detrimental effect is reduced by ~4 orders of magnitude through the coherent addition of Stokes and anti-Stokes reflections from two counter-propagating BDGs in the fiber. The technique advantageously combines the high-spatial-resolution of BDGs reflectometry with the increased tolerance to optical power fluctuations of phasorial measurements, to enhance the performance of fiber-optic strain sensors. We demonstrate a distributed measurement (20cm spatial-resolution) of both static and dynamic (5kHz of vibrations at a sampling rate of 1MHz) strain fields acting on the fiber, in good agreement with theory and (for the static case) with the results of commercial reflectometers.