  In a previous paper, we presented an extension of our reflection model
RELXILL_NK to include the finite thickness of the accretion disk following the
prescription in Taylor & Reynolds (2018). In this paper, we apply our model to
fit the 2013 simultaneous observations by NuSTAR and XMM-Newton of the
supermassive black hole in MCG-06-30-15 and the 2019 NuSTAR observation of the
Galactic black hole in EXO 1846-031. The high-quality data of these spectra had
previously led to precise black hole spin measurements and very stringent
constraints on possible deviations from the Kerr metric. We find that the disk
thickness does not change previous spin results found with a model employing an
infinitesimally thin disk, which confirms the robustness of spin measurements
in high radiative efficiency disks, where the impact of disk thickness is
minimal. Similar analysis on lower accretion rate systems will be an important
test for measuring the effect of disk thickness on black hole spin
measurements.
