When competing campaigns target a population of large language model (LLM) agents, observed opinion changes may reflect both campaign influence and changes that would occur without intervention. We study how the timing of campaign expenditure and the population's own evolution shape outcomes in a network of persona-conditioned LLM agents that exchange and revise opinions in natural language. A proponent and a challenger are tasked with generating opposing messages under equal delivery budgets, while a separate stance probe measures opinions without influencing the simulation. Across eight claims, we compare single-campaign and competitive conditions against matched no-campaign runs, and evaluate all nine combinations of early, sustained, and late spending on a reference topic. Baseline stance drift varies substantially across claims and, on some, accounts for a sizeable fraction of apparent campaign effects. After accounting for this drift, the direction of observed campaign-associated changes aligns more closely with the claim's epistemic standing than with the campaigner's assigned role. Uninfluenced populations also consistently lose stance diversity, demonstrating that directional opinion change and convergence are distinct phenomena. In networks with two opinion-segregated communities, campaigns primarily reduce differences between communities rather than diversity within them. LLM campaign agents do not always argue for their assigned positions, particularly when these conflict with established evidence. Finally, campaign outcomes depend on the opponent's expenditure schedule: unlike a matched numerical bounded-confidence population receiving interventions at the same times and locations, the LLM population exhibits a payoff structure with no pure-strategy equilibrium.

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