Recent advancements in Large Language Models (LLMs) have demonstrated remarkable capabilities in reasoning, reflection, and tool utilization, unlocking new paradigms for automating complex engineering workflows. However, in the domain of sequential recommendation (SR), tuning models on new datasets still relies heavily on the manual trial-and-error of experienced machine learning engineers. To bridge this gap, we propose \textbf{VirtualMLE}, an LLM-agent framework that leverages the cognitive capabilities of LLMs to organize recommender optimizing into a closed loop of execution, reflection, and memory update. After each trial, the agent explicitly analyzes the observed outcomes and stores concise heuristic feedback in a hierarchical memory system. We evaluate VirtualMLE on three Amazon SR benchmarks with two representative backbones, SASRec and HSTU. VirtualMLE reaches competitive recommendation quality with substantially fewer trials. Furthermore, we observe that cognition summaries distilled from previous datasets can significantly accelerate the search process on unseen datasets, demonstrating the potential of transferring tuning heuristics. Overall, our results provide compelling evidence that LLM agents equipped with reflection and memory can serve as practical virtual engineers to automate and amortize heuristic learning in SR optimization. Our codes are available.