The growing demand for on-device large language model (LLM) inference highlights the need for efficient mobile edge computing (MEC) solutions, especially in resource-constrained settings. Speculative decoding offers a promising solution by partitioning token generation between a lightweight draft model on mobile devices and a powerful target model on edge servers, but suffers from communication overhead and asynchronous delays. This paper is the first to propose a unified framework that jointly optimizes user association and resource allocation (UARA) to support efficient parallel speculative decoding. We solve the UARA problem using a multi-agent deep reinforcement learning algorithm. To evaluate our approach under realistic conditions, we conduct experiments using the Sionna simulator. Results show that our method achieves up to 28.0% and an average of 23.7% reduction in end-to-end latency without compromising inference accuracy, enabling scalable and low-latency LLM services in MEC systems.