Herbicide resistance in Palmer amaranth (Amaranthus palmeri S. Watson) continues to threaten the sustainability of cotton (Gossypium hirsutum L.) production in the U.S., partly because management programs often emphasize in-season suppression without sufficiently limiting the number of individuals repeatedly exposed to postemergence herbicide selection. A five-year large-plot field experiment (2019–2023) was conducted to evaluate four integrated weed management (IWM) components, zero tolerance for seedbank replenishment (ZT–SBR), occasional deep inversion tillage (Occ_DIT), cereal rye cover crop (CRCC), and dicamba-inclusive herbicide programs (Dic_inCrop), applied singly, in combination, or absent altogether in a conventional four-pass base program lacking all four components. Preemergence escapes, defined here as emerged A. palmeri surviving the residual herbicide preceding each pass, were quantified at each timing and analyzed as annual trajectories and five-year cumulative exposure (a proxy for accumulated postemergence selection). In 2024, legacy emergence was measured under unmanaged conditions. Occ_DIT strongly structured temporal trajectories, inducing an immediate low-density state (12% of the base program in Year 1) versus gradual decline without Occ_DIT (∼75% in Year 1; steep early slope), yielding markedly lower cumulative preemergence-escape pressure. Across five years, cumulative exposure was most reduced by Occ_DIT, followed by Dic_inCrop, CRCC, and ZT–SBR, with significant interactions indicating non-additive benefits. In the legacy year, main-effect incidence rate ratios (IRRs) showed substantial suppression by Dic_inCrop (IRR = 0.02), ZT–SBR (IRR = 0.02), Occ_DIT (IRR = 0.06), and CRCC (IRR = 0.24), with four-way combinations reducing emergence by >98% relative to the base program. Positive interaction IRRs reflected diminishing marginal returns near the ecological floor, not antagonism. Collectively, these results demonstrate that IWM efficacy at low weed densities is governed less by additive suppression than by how mortality is repartitioned across independent demographic bottlenecks, reinforcing the value of diversified IWM as an evolutionary risk-management strategy.