  PSR J1933$-$6211 is a 3.5-ms pulsar in a 12.8-d orbit with a white dwarf
(WD). Its high proper motion and low dispersion measure result in such
significant interstellar scintillation that high signal-to-noise detections
require long observing durations or fortuitous timing. We turn to the sensitive
MeerKAT telescope and, combined with historic Parkes data, leverage PSR
J1933$-$6211's kinematic and relativistic effects to constrain its 3D orbital
geometry and the component masses. We obtain precise proper motion and parallax
estimates, and measure their effects as secular changes in the Keplerian
orbital parameters: a variation in orbital period of $7(1) \times 10^{-13}$ s
s$^{-1}$ and a change in projected semi-major axis of $1.60(5) \times 10^{-14}$
s s$^{-1}$. A self-consistent analysis of all kinematic and relativistic
effects yields a distance of $1.6^{+0.2}_{-0.3}$ kpc, an orbital inclination,
$i = 55(1)$ deg and a longitude of the ascending node, $\Omega =
255^{+8}_{-14}$ deg. The probability densities for $\Omega$ and $i$ and their
symmetric counterparts, ($180-i$, $360-\Omega$), are seen to depend on the
fiducial orbit used to measure the time of periastron passage. We investigate
this unexpected dependence and rule out software-related causes using
simulations. Nevertheless, we constrain the pulsar and WD masses to
$1.4^{+0.3}_{-0.2}$ M$_\odot$ and $0.43(5)$ M$_\odot$ respectively. These
strongly disfavour a helium-dominated WD. The orbital similarities between PSRs
J1933$-$6211 and J1614$-$2230 suggest they underwent Case A Roche lobe
overflow, an extended evolution while the companion star is still on the Main
Sequence. However, with a mass of $\sim 1.4$ M$_\odot$, PSR J1933$-$6211 has
not accreted significant matter. This highlights the low accretion efficiency
of the spin-up process and suggests that observed neutron star masses are
mostly a result of supernova physics.
