Rapidity-even directed flow, $v\_{1}^{\rm even}$, provides a sensitive probe of fluctuation-driven dipolar asymmetry in relativistic heavy-ion collisions, but its extraction is complicated by strong first-harmonic non-flow correlations, particularly those associated with global momentum conservation (GMC). In this study, $v\_{1}^{\rm even}$ and its multi-particle correlations are investigated in Au+Au collisions at $\sqrt{s\_NN}=200$~GeV using the AMPT and HIJING models. An $\eta$-dependent weighting procedure is applied to suppress the leading GMC contribution. The GMC-suppressed HIJING results are strongly reduced for most $v_1$-related observables, while AMPT reproduces the characteristic sign-changing $p_T$ dependence of $v_{1}^{\rm even}$ and exhibits clear sensitivity to the partonic transport setting. The non-normalized mixed-harmonic correlations show a stronger transport dependence, whereas the normalized observables are substantially less sensitive to the absolute final-state response. Comparison with the initial-state eccentricity correlations shows that these normalized observables retain the underlying dipolar, elliptic, and triangular correlation structure after modification by the medium. These results demonstrate that GMC-suppressed rapidity-even dipolar flow correlations provide complementary constraints on initial-state fluctuations and their transformation during the final-state evolution.