  We present the development of high-performance polarized $^3\mathrm{He}$
targets for use in electron scattering experiments that utilize the technique
of alkali-hybrid spin-exchange optical pumping. We include data obtained during
the characterization of 24 separate target cells, each of which was constructed
while preparing for one of four experiments at Jefferson Laboratory in Newport
News, Virginia. The results presented here document dramatic improvement in the
performance of polarized $^3\mathrm{He}$ targets, as well as the target
properties and operating parameters that made those improvements possible.
Included in our measurements were determinations of the so-called $X$-factors
that quantify a temperature-dependent and as-yet poorly understood
spin-relaxation mechanism that limits the maximum achievable $^3\mathrm{He}$
polarization to well under 100%. The presence of this spin-relaxation mechanism
was clearly evident in our data. We also present results from a simulation of
the alkali-hydrid spin-exchange optical pumping process that was developed to
provide guidance in the design of these targets. Good agreement with actual
performance was obtained by including details such as off-resonant optical
pumping. Now benchmarked against experimental data, the simulation is useful
for the design of future targets. Included in our results is a measurement of
the $\mathrm{K}$-$^3\mathrm{He}$ spin-exchange rate coefficient
$k^\mathrm{K}_\mathrm{se} = \left ( 7.46 \pm 0.62 \right )\!\times\!10^{-20}\
\mathrm{cm^3/s}$ over the temperature range 503 K to 563 K.
