  Heavy diatomic molecules have been identified as good candidates for use in
electron electric dipole moment (eEDM) searches. Suitable molecular species can
be produced in pulsed beams, but with a total flux and/or temporal evolution
that varies significantly from pulse to pulse. These variations can degrade the
experimental sensitivity to changes in spin precession phase of an electri-
cally polarized state, which is the observable of interest for an eEDM
measurement. We present two methods for measurement of the phase that provide
immunity to beam temporal variations, and make it possible to reach
shot-noise-limited sensitivity. Each method employs rapid projection of the
spin state onto both components of an orthonormal basis. We demonstrate both
methods using the eEDM-sensitive H state of thorium monoxide (ThO), and use one
of them to measure the magnetic moment of this state with increased accuracy
relative to previous determinations.
