  We carry out simulated annealing and employ a generalized Kibble-Zurek
scaling hypothesis to study the 2D Ising spin glass with normal-distributed
couplings. The system has an equilibrium glass transition at temperature $T=0$.
From a scaling analysis when $T\rightarrow 0$ at different annealing
velocities, we extract the dynamic critical exponent $z$, i.e., the exponent
relating the relaxation time $\tau$ to the system length $L$; $\tau\sim L^z$.
We find $z=13.6 \pm 0.4$ for both the Edwards-Anderson spin-glass order
parameter and the excess energy. This is different from a previous study of the
system with bimodal couplings [S. J. Rubin, N. Xu, and A. W. Sandvik, Phys.
Rev. E {\bf 95}, 052133 (2017)] where the dynamics is faster and the above two
quantities relax with different exponents (and that of the energy is larger).
We here argue that the different behaviors arise as a consequence of the
different low-energy landscapes---for normal-distributed couplings the ground
state is unique (up to a spin reflection) while the system with bimodal
couplings is massively degenerate. Our results reinforce the conclusion of
anomalous entropy-driven relaxation behavior in the bimodal Ising glass. In the
case of a continuous coupling distribution, our results presented here indicate
that, although Kibble-Zurek scaling holds, the perturbative behavior normally
applying in the slow limit breaks down, likely due to quasi-degenerate states,
and the scaling function takes a different form.
