LLM-driven program evolution can discover high-quality programs, but its cost and run-to-run variance hinder reliable progress. We propose TurboEvolve, a multi-island evolutionary framework that improves sample efficiency and robustness under fixed evaluation budgets. Inspired by the multiple-offspring strategy in evolutionary algorithms, TurboEvolve introduces verbalized Sampling, prompting the LLM to emit K diverse candidates with explicit self-assigned sampling weights, and an online scheduler that adapts K to expand exploration under stagnation and reduce overhead during steady progress. To exploit existing solution pools, we further propose "seed-pool injection," which clusters seeds and assigns them across islands with controlled perturbations and elitist preservation to balance diversity and refinement. Across multiple program-optimization benchmarks, TurboEvolve consistently achieves stronger performance at lower budgets and improves best-known solutions on several tasks.