The combination of galaxy-galaxy lensing (GGL) and galaxy clustering is a powerful probe of low redshift matter clustering, especially if it is extended to the non-linear regime. To this end, we use an N-body and halo occupation distribution (HOD) emulator method to model the redMaGiC sample of colour-selected passive galaxies in the Dark Energy Survey (DES), adding parameters that describe central galaxy incompleteness, galaxy assembly bias, and a scale-independent multiplicative lensing bias $A_\mathrm{lens}$. We use this emulator to forecast cosmological constraints attainable from the GGL surface density profile $\Delta\Sigma(r_p)$ and the projected galaxy correlation function $w_{p,gg}(r_p)$ in the final (Year 6) DES data set over scales $r_p=0.3-30.0 , h^{-1} , Mpc$. For a $3%$ prior on $A_{lens}$ we forecast precisions of $1.9%$, $2.0%$, and $1.9%$ on $\Omega_m$, $\sigma_8$, and $S_8 \equiv \sigma_8\Omega_m^{0.5}$, marginalized over all halo occupation distribution (HOD) parameters as well as $A_\mathrm{lens}$. Adding scales $r_p=0.3-3.0 , h^{-1} , Mpc$ improves the $S_8$ precision by a factor of ${\sim}1.6$ relative to a large scale ($3.0-30.0 , h^{-1} , Mpc$) analysis, equivalent to increasing the survey area by a factor of ${\sim}2.6$. Sharpening the $A_\mathrm{lens}$ prior to $1%$ further improves the $S_8$ precision to $1.1%$, and it amplifies the gain from including non-linear scales. Our emulator achieves percent-level accuracy similar to the projected DES statistical uncertainties, demonstrating the feasibility of a fully non-linear analysis. Obtaining precise parameter constraints from multiple galaxy types and from measurements that span linear and non-linear clustering offers many opportunities for internal cross-checks, which can diagnose systematics and demonstrate the robustness of cosmological results.