  We test the hypothesis that the observed first-peak (Sr, Y, Zr) and
second-peak (Ba) s-process elemental abundances in low metallicity Milky Way
stars ($\text{[Fe/H]} \lesssim -0.5$), and the abundances of the intervening
elements Mo and Ru, can be explained by a pervasive r-process contribution that
originates in neutrino-driven winds from highly-magnetic and rapidly rotating
proto-neutron stars (proto-NSs). To this end, we construct chemical evolution
models that incorporate recent calculations of proto-NS yields in addition to
contributions from AGB stars, Type Ia supernovae, and two alternative sets of
yields for massive star winds and core collapse supernovae. For non-rotating
massive star yields from either set, models without proto-NS winds underpredict
the observed s-process peak abundances by $0.3$-$1\,\text{dex}$ at low
metallicity, and they severely underpredict Mo and Ru at all metallicities.
Models that include the additional wind yields predicted for proto-NSs with
spin periods $P \sim 2$-$5\,\text{ms}$ fit the observed trends for all these
elements well. Alternatively, models that omit proto-NS winds but adopt yields
of rapidly rotating massive stars, with $v_{\rm rot}$ between $150$ and
$300\,\text{km}\,\text{s}^{-1}$, can explain the observed abundance levels
reasonably well for $\text{[Fe/H]}<-2$. These models overpredict [Sr/Fe] and
[Mo/Fe] at higher metallicities, but with a tuned dependence of $v_{\rm rot}$
on stellar metallicity they might achieve an acceptable fit at all [Fe/H]. If
many proto-NSs are born with strong magnetic fields and short spin periods,
then their neutrino-driven winds provide a natural source for Sr, Y, Zr, Mo,
Ru, and Ba in low metallicity stellar populations. Spherical winds from
unmagnetized proto-NSs, on the other hand, overproduce the observed Sr, Y, and
Zr abundances by a large factor.
