Experimental searches for the electron electric-dipole moment (EDM) probe new physics beyond the standard model. The current best EDM limit was set by the ACME Collaboration [Science 343, 269 (2014)], constraining time-reversal symmetry (T) violating physics at the TeV energy scale. ACME used optical pumping to prepare a coherent superposition of ThO H-3 Delta(1) states that have aligned electron spins. Spin precession due to the molecule s internal electric field was measured to extract the EDM. We report here on an improved method for preparing this spin-aligned state of the electron by using stimulated Raman adiabatic passage (STIRAP). We demonstrate a transfer efficiency of 75% +/- 5%, representing a significant gain in signal for a next-generation EDM experiment. We discuss the particularities of implementing STIRAP in systems such as ours, where molecular ensembles with large phase-space distributions are transferred via weak molecular transitions with limited laser power and limited optical access.