Neural network-based molecular dynamics (NNMD) simulations incorporating long-range electrostatic interactions have significantly extended the applicability to heterogeneous and ionic systems, enabling effective modeling critical physical phenomena such as protein folding and dipolar surface and maintaining ab initio accuracy. However, neural network inference and long-range force computation remain the major bottlenecks, severely limiting simulation speed. In this paper, we target DPLR, a state-of-the-art NNMD package that supports long-range electrostatics, and propose a set of comprehensive optimizations to enhance computational efficiency. We introduce (1) a hardware-offloaded FFT method to reduce the communication overhead; (2) an overlapping strategy that hides long-range force computations using a single core per node, and (3) a ring-based load balancing method that enables atom-level task evenly redistribution with minimal communication overhead. Experimental results on the Fugaku supercomputer show that our work achieves a 37x performance improvement, reaching a maximum simulation speed of 51 ns/day.