  We consider 1+3-dimensional domain wall solutions of heterotic supergravity
on a six-dimensional warped nearly K\"ahler manifold $X_6$ in the presence of
gravitational and gauge instantons of tanh-kink type as constructed in
[arXiv:1109.3552]. We include first order $\alpha'$ corrections to the
heterotic supergravity action, which imply a non-trivial Yang-Mills sector and
Bianchi identity. We present a variety of solutions, depending on the choice of
instantons, for the special case in which the SU(3) structure on $X_6$
satisfies $W_1^-=0$. The solutions preserve two real supercharges, which
corresponds to $\mathcal{N}{=}1/2$ supersymmetry from the four-dimensional
point of view. Besides serving as a useful framework for collecting existing
solutions, the formulation in terms of dynamic SU(3) structures utilized here
allows us to obtain new solutions in as yet unexplored corners of the instanton
configuration space. Our approach thus offers a unified description of the
embedding of tanh-kink-type instantons into half-BPS solutions of heterotic
supergravity where the internal six-dimensional manifold has a warped nearly
K\"ahler geometry
