  We present a re-analysis of cosmic shear and galaxy clustering from
first-year Dark Energy Survey data (DES Y1), making use of a Hybrid Effective
Field Theory (HEFT) approach to model the galaxy-matter relation on weakly
non-linear scales, initially proposed in Modi et al. (2020) (arXiv:1910.07097).
This allows us to explore the enhancement in cosmological constraining power
enabled by extending the galaxy clustering scale range typically used in
projected large-scale structure analyses. Our analysis is based on a recomputed
harmonic-space data vector and covariance matrix, carefully accounting for all
sources of mode-coupling, non-Gaussianity and shot noise, which allows us to
provide robust goodness-of-fit measures. We use the \textsc{AbacusSummit} suite
of simulations to build an emulator for the HEFT model predictions. We find
that this model can explain the galaxy clustering and shear data up to
wavenumbers $k_{\rm max}\sim 0.6\, {\rm Mpc}^{-1}$. We constrain
$(S_8,\Omega_m) = (0.786\pm 0.020,0.273^{+0.030}_{-0.036})$ at the fiducial
$k_{\rm max}\sim 0.3\, {\rm Mpc}^{-1}$, improving to $(S_8,\Omega_m) =
(0.786^{+0.015}_{-0.018},0.266^{+0.024}_{-0.027})$ at $k_{\rm max}\sim 0.5\,
{\rm Mpc}^{-1}$. This represents a $\sim10\%$ and $\sim35\%$ improvement on the
constraints derived respectively on both parameters using a linear bias
relation on a reduced scale range ($k_{\rm max}\lesssim0.15\,{\rm Mpc}^{-1}$),
in spite of the 15 additional parameters involved in the HEFT model. We
investigate whether HEFT can be used to constrain the Hubble parameter and find
$H_0= 70.7_{-3.5}^{+3.0}\,{\rm km}\,s^{-1}\,{\rm Mpc}^{-1}$. Our constraints
are investigative and subject to certain caveats discussed in the text.
