  We present follow-up spectroscopy and a detailed model atmosphere analysis of
29 wide double white dwarfs, including eight systems with a crystallized C/O
core member. We use state-of-the-art evolutionary models to constrain the
physical parameters of each star, including the total age. Assuming that the
members of wide binaries are coeval, any age difference between the binary
members can be used to test the cooling physics for white dwarf stars,
including potential delays due to crystallization and $^{22}$Ne distillation.
We use our control sample of 14 wide binaries with non-crystallized members to
show that this method works well; the control sample shows an age difference of
only $\Delta$Age = $-0.03 \pm$ 0.15 Gyr between its members. For the eight
crystallized C/O core systems we find a cooling anomaly of $\Delta$Age=
1.13$^{+1.20}_{-1.07}$ Gyr. Even though our results are consistent with a small
additional cooling delay ($\sim1$ Gyr) from $^{22}$Ne distillation and other
neutron-rich impurities, the large uncertainties make this result not
statistically significant. Nevertheless, we rule out cooling delays longer than
3.6 Gyr at the 99.7% ($3\sigma$) confidence level for 0.6-0.9 $M_{\odot}$ white
dwarfs. Further progress requires larger samples of wide binaries with
crystallized massive white dwarf members. We provide a list of subgiant + white
dwarf binaries that could be used for this purpose in the future.
