The Galactic 1.809-MeV γ-ray signature from the β decay of ^{26g}Al is a dominant target of γ-ray astronomy, of which a significant component is understood to originate from massive stars. The ^{26g}Al(p,γ)^{27}Si reaction is a major destruction pathway for ^{26g}Al at stellar temperatures, but the reaction rate is poorly constrained due to uncertainties in the strengths of low-lying resonances in ^{27}Si. The ^{26g}Al(d,p)^{27}Al reaction has been employed in inverse kinematics to determine the spectroscopic factors, and hence resonance strengths, of proton resonances in ^{27}Si via mirror symmetry. The strength of the 127-keV resonance is found to be a factor of 4 higher than the previously adopted upper limit, and the upper limit for the 68-keV resonance has been reduced by an order of magnitude, considerably constraining the ^{26g}Al destruction rate at stellar temperatures.