  We describe a new method for determining total gas-phase abundances for the
Galactic ISM with minimal ionization uncertainties. For sight lines toward
globular clusters containing both UV-bright stars and radio pulsars, one can
measure column densities of HI and several metal ions using UV absorption
measurements and of H II using radio dispersion measurements, thereby
minimizing ionization uncertainties. We apply this method to the globular
cluster Messier 3 sight line using FUSE and HST ultraviolet spectroscopy of the
post-asymptotic giant branch star von Zeipel 1128 and radio observations by
Ransom et al. of millisecond pulsars. Ionized hydrogen is 45+/-5% of the total
along this sight line, the highest measured fraction along a high-latitude
pulsar sight line. We derive total gas-phase abundances log N(S)/N(H) =
-4.87+/-0.03 and log N(Fe)/N(H) = -5.27+/-0.05. Our derived sulfur abundance is
in excellent agreement with recent solar system determinations of Asplund,
Grevesse, & Sauval, but -0.14 dex below the solar system abundance typically
adopted in studies of the ISM. The iron abundance is ~-0.7 dex below the solar
system abundance, consistent with significant depletion. Abundance estimates
derived by simply comparing S II and Fe II to H I are +0.17 and +0.11 dex
higher, respectively, than our measurements. Ionization corrections to the
gas-phase abundances measured in the standard way are, therefore, significant
compared with the measurement uncertainties along this sight line. The
systematic uncertainties associated with the uncertain contribution to the
electron column density from ionized helium could raise these abundances by
<+0.03 dex (+7%). [Abridged]
