We present a detailed analysis of two well-localized, highly offset short gamma-ray bursts---GRB~070809 and GRB~090515---investigating the kinematic evolution of their progenitors from compact object formation until merger. Calibrating to observations of their most probable host galaxies, we construct semi-analytic galactic models that account for star formation history and galaxy growth over time. We pair detailed kinematic evolution with compact binary population modeling to infer viable post-supernova velocities and inspiral times. By populating binary tracers according to the star formation history of the host and kinematically evolving their post-supernova trajectories through the time-dependent galactic potential, we find that systems matching the observed offsets of the bursts require post-supernova systemic velocities of hundreds of kilometers per second. Marginalizing over uncertainties in the stellar mass--halo mass relation, we find that the second-born neutron star in the GRB~070809 and GRB~090515 progenitor systems received a natal kick of $gtrsim 200~mathrm{km,s}^{-1}$ at the 78% and 91% credible levels, respectively. Applying our analysis to the full catalog of localized short gamma-ray bursts will provide unique constraints on their progenitors and help unravel the selection effects inherent to observing transients that are highly offset with respect to their hosts.
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