  With unparalleled rotational stability, millisecond pulsars (MSPs) serve as
ideal laboratories for numerous astrophysical studies, many of which require
precise knowledge of the distance and/or velocity of the MSP. Here, we present
the astrometric results for 18 MSPs of the "MSPSR$\pi$" project focusing
exclusively on astrometry of MSPs, which includes the re-analysis of 3
previously published sources. On top of a standardized data reduction protocol,
more complex strategies (i.e., normal and inverse-referenced 1D interpolation)
were employed where possible to further improve astrometric precision. We
derived astrometric parameters using sterne, a new Bayesian astrometry
inference package that allows the incorporation of prior information based on
pulsar timing where applicable. We measured significant ($>3\,\sigma$)
parallax-based distances for 15 MSPs, including $0.81\pm0.02\,$kpc for PSR
J1518+4904 -- the most significant model-independent distance ever measured for
a double neutron star system. For each MSP with a well-constrained distance, we
estimated its transverse space velocity and radial acceleration. Among the
estimated radial accelerations, the updated ones of PSR J1012+5307 and PSR
J1738+0333 impose new constraints on dipole gravitational radiation and the
time derivative of Newton's gravitational constant. Additionally, significant
angular broadening was detected for PSR J1643-1224, which offers an independent
check of the postulated association between the HII region Sh 2-27 and the main
scattering screen of PSR J1643-1224. Finally, the upper limit of the death line
of $\gamma$-ray-emitting pulsars is refined with the new radial acceleration of
the hitherto least energetic $\gamma$-ray pulsar PSR J1730-2304.
