  We study Jackiw-Teitelboim gravity with dynamical end of the world branes in
asymptotically nearly AdS$_2$ spacetimes. We quantize this theory in Lorentz
signature, and compute the Euclidean path integral summing over topologies
including dynamical branes. The latter will be seen to exactly match with a
modification of the SSS matrix model. The resolution of UV divergences in the
gravitational instantons involving the branes will lead us to understand the
matrix model interpretation of the Wilsonian effective theory perspective on
the gravitational theory. We complete this modified SSS matrix model
nonperturbatively by extending the integration contour of eigenvalues into the
complex plane. Furthermore, we give a new interpretation of other phases in
such matrix models. We derive an effective $W(\Phi)$ dilaton gravity, which
exhibits similar physics semiclassically. In the limit of a large number of
flavors of branes, the effective extremal entropy $S_{0,\text{eff}}$ has the
form of counting the states of these branes.
