  The Galactic center excess (GCE) remains one of the most intriguing
discoveries from the Fermi Large Area Telescope (LAT) observations. We revisit
the characteristics of the GCE by first producing a new set of high-resolution
galactic diffuse gamma-ray emission templates, which are ultimately due to
cosmic-ray interactions with the interstellar medium. Using multi-messenger
observations we constrain the properties of the galactic diffuse emission. The
broad properties of the GCE that we find in this work are qualitatively
unchanged despite the introduction of this new set of templates, though its
quantitative features appear mildly different than those obtained in previous
analyses. In particular, we find a high-energy tail at higher significance than
previously reported. This tail is very prominent in the northern hemisphere,
and less so in the southern hemisphere. This strongly affects one prominent
interpretation of the excess: known millisecond pulsars are incapable of
producing this high-energy emission, even in the relatively softer southern
hemisphere, and are therefore disfavored as the sole explanation of the GCE.
The annihilation of dark matter particles of mass $40^{+10}_{-7}$ GeV (95$\%$
CL) to $b$ quarks with a cross-section of $\sigma v = 1.4^{+0.6}_{-0.3} \times
10^{-26}$ cm$^{3}$s$^{-1}$ provides a good fit to the excess especially in the
relatively cleaner southern sky. Dark matter of the same mass range
annihilating to $b$ quarks or heavier dark matter particles annihilating to
heavier Standard Model bosons can combine with millisecond pulsars to provide a
good fit to the southern hemisphere emission. As part of this paper, we make
publicly available all of our templates and the data covariance matrix we have
generated to account for systematic uncertainties.[abridged]
