  This study constitutes part of a larger effort aimed at better characterizing
the Galactic globular clusters (GGCs) located towards the inner Milky Way bulge
and disk. Here, we focus on internal kinematics of nine GGCs, obtained from
space-based imaging over time baselines of $>$9 years. We exploit multiple
avenues to assess the dynamical state of the target GGCs, constructing radial
profiles of projected stellar density, proper motion dispersion, and
anisotropy. We posit that two-thirds (6/9) of our target GGCs are in an
advanced dynamical state, and are close to (or have recently undergone) core
collapse, supported by at least two lines of evidence: First, we find
relatively steep proper motion dispersion profiles, in accord with literature
values for core-collapsed GGCs. Second, we find that our sample is, in the
mean, isotropic even out to their half-light radii, although one of our target
clusters (NGC 6380) is tangentially anisotropic at $>$1$\sigma$ beyond its
half-light radius, in accord with theoretical predictions for clusters evolving
in strong tidal fields. Our proper motion dispersion and anisotropy profiles
are made publicly available.
