Population health initiatives often rely on cold outreach to close gaps in preventive care, such as overdue screenings or immunizations. Tailoring messages to diverse patient populations remains challenging, as traditional A/B testing requires large sample sizes to test only two alternative messages. With increasing availability of large language models (LLMs), programs can utilize tiered testing among both LLM and manual human agents, presenting the dilemma of identifying which patients need different levels of human support to cost-effectively engage large populations. Using microsimulations, we compared both the statistical power and false positive rates of A/B testing and Sequential Multiple Assignment Randomized Trials (SMART) for developing personalized communications across multiple effect sizes and sample sizes. SMART showed better cost-effectiveness and net benefit across all scenarios, but superior power for detecting heterogeneous treatment effects (HTEs) only in later randomization stages, when populations were more homogeneous and subtle differences drove engagement differences.