  One of the most important parameters in characterizing the Epoch of
Reionization, the escape fraction of ionizing photons, $f_\mathrm{esc}$,
remains unconstrained both observationally and theoretically. With recent work
highlighting the impact of galaxy-scale feedback on the instantaneous value of
$f_\mathrm{esc}$, it is important to develop a model in which reionization is
self-consistently coupled to galaxy evolution. In this work, we present such a
model and explore how physically motivated functional forms of $f_\mathrm{esc}$
affect the evolution of ionized hydrogen within the intergalactic medium. Using
the $21$cm power spectrum evolution, we investigate the likelihood of
observationally distinguishing between a constant $f_\mathrm{esc}$ and other
models that depend upon different forms of galaxy feedback. We find that
changing the underlying connection between $f_\mathrm{esc}$ and galaxy feedback
drastically alters the large-scale $21$cm power. The upcoming Square Kilometre
Array Low Frequency instrument possesses the sensitivity to differentiate
between our models at a fixed optical depth, requiring only $200$ hours of
integration time focused on redshifts $z = 7.5-8.5$. Generalizing these results
to account for a varying optical depth will require multiple $800$ hour
observations spanning redshifts $z = 7-10$. This presents an exciting
opportunity to observationally constrain one of the most elusive parameters
during the Epoch of Reionization.
