  The Milky Way hosts a hot ($\approx 2 \times 10^6$ K), diffuse, gaseous halo
based on detections of z = 0 OVII and OVIII absorption lines in quasar spectra
and emission lines in blank-sky spectra. Here we improve constraints on the
structure of the hot gas halo by fitting a radial model to a much larger sample
of OVII and OVIII emission line measurements from XMM-Newton EPIC-MOS spectra
compared to previous studies ($\approx$ 650 sightlines). We assume a modified
$\beta$-model for the halo density distribution and a constant-density Local
Bubble from which we calculate emission to compare with the observations. We
find an acceptable fit to the OVIII emission line observations with
$\chi^{2}_{red}$ (dof) = 1.08 (644) for best-fit parameters of $n_o
r_c^{3\beta} = 1.35 \pm 0.24$ cm$^{-3}$ kpc$^{3\beta}$ and $\beta = 0.50 \pm
0.03$ for the hot gas halo and negligible Local Bubble contribution. The OVII
observations yield an unacceptable $\chi^{2}_{red}$ (dof) = 4.69 (645) for
similar best-fit parameters, which is likely due to temperature or density
variations in the Local Bubble. The OVIII fitting results imply hot gas masses
of $M$(< 50 kpc) = $3.8_{-0.3}^{+0.3} \times 10^{9} M_{\odot}$ and $M$(< 250
kpc) = $4.3_{-0.8}^{+0.9} \times 10^{10} M_{\odot}$, accounting for $\lesssim$
50% of the Milky Way's missing baryons. We also explore our results in the
context of optical depth effects in the halo gas, the halo gas cooling
properties, temperature and entropy gradients in the halo gas, and the gas
metallicity distribution. The combination of absorption and emission line
analyses implies a sub-solar gas metallicity that decreases with radius, but
that also must be $\geq 0.3 Z_{\odot}$ to be consistent with the pulsar
dispersion measure toward the LMC.
