In the era of large language models (LLMs), supervised neural methods remain the state-of-the-art (SOTA) for Coreference Resolution. Yet, their full potential is underexplored, particularly in incremental clustering, which faces the critical challenge of balancing efficiency with performance for long texts. To address the limitation, we propose \textbf{MEIC-DT}, a novel dual-threshold, memory-efficient incremental clustering approach based on a lightweight Transformer. MEIC-DT features a dual-threshold constraint mechanism designed to precisely control the Transformer's input scale within a predefined memory budget. This mechanism incorporates a Statistics-Aware Eviction Strategy (\textbf{SAES}), which utilizes distinct statistical profiles from the training and inference phases for intelligent cache management. Furthermore, we introduce an Internal Regularization Policy (\textbf{IRP}) that strategically condenses clusters by selecting the most representative mentions, thereby preserving semantic integrity. Extensive experiments on common benchmarks demonstrate that MEIC-DT achieves highly competitive coreference performance under stringent memory constraints.