Precision spectroscopy of molecules is complementary to studies with high-energy colliders in the pursuit of physics beyond the Standard Model. Our search for an electric dipole moment in an electron (eEDM) constitutes a background free measurement of T-symmetry violation, attempting to explain the matter/antimatter asymmetry in the Universe. We choose to study molecular ions, which are easily trappable, allowing us to select species such as HfF+ that have enhanced sensitivity to the eEDM and simultaneously benefit from long interrogation times. We have recently attained >2 s spin-coherence duration and a 20-fold increase in ion count rate for our next generation measurement. I will discuss the noise-immune detection scheme we developed to reach the quantum projection noise limit in our measurement, overcoming technical noise that becomes proportionally more significant in our newly achieved large samples. Overall, we demonstrate a 40-fold improvement in our sensitivity, which will make our upcoming measurement competitive with the current upper limit set on the eEDM. The advantages of studies using trapped molecular ions may help solve many fundamental questions in physics and chemistry, and the precise quantum state preparation and readout schemes we develop pave the road toward such realizations.