  Mutual gravitation between a pulsating star and an orbital companion leads to
a time-dependent variation in path length for starlight traveling to Earth.
These variations can be used for coherently pulsating stars, such as the
{\delta} Scuti variables, to constrain the masses and orbits of their
companions. Observing these variations for {\delta} Scuti stars has previously
relied on subdividing the light curve and measuring the average pulsation phase
in equally sized subdivisions, which leads to under-sampling near periapsis. We
introduce a new approach that simultaneously forward-models each sample in the
light curve and show that this method improves upon current sensitivity limits
- especially in the case of highly eccentric and short-period binaries. We find
that this approach is sensitive enough to observe Jupiter mass planets around
{\delta} Scuti stars under ideal conditions, and use gravity-mode pulsations in
the subdwarf B star KIC 7668647 to detect its companion without radial velocity
data. We further provide robust detection limits as a function of the SNR of
the pulsation mode and determine that the minimum detectable light travel time
amplitude for a typical Kepler {\delta} Scuti is around 2 s. This new method
significantly enhances the application of light travel time variations to
detecting short period binaries with pulsating components, and pulsating A-type
exoplanet host stars, especially as a tool for eliminating false positives.
