AI-driven methods have demonstrated considerable success in tackling the central challenge of accurately solving the Schrödinger equation for complex many-body systems. Among neural network quantum state (NNQS) approaches, the NNQS-SCI (Selected Configuration Interaction) method stands out as a state-of-the-art technique, recognized for its high accuracy and scalability. However, its application to larger systems is severely constrained by a hybrid CPU-GPU architecture. Specifically, centralized CPU-based global de-duplication creates a severe scalability barrier due to communication bottlenecks, while host-resident coupled-configuration generation induces prohibitive computational overheads. We introduce QiankunNet-cuSCI, a fully GPU-accelerated SCI framework designed to overcome these bottlenecks. It first integrates a distributed, load-balanced global de-duplication algorithm to minimize redundancy and communication overhead at scale. To address compute limitations, it employs specialized, fine-grained CUDA kernels for exact coupled configuration generation. Finally, to break the single-GPU memory barrier exposed by this full acceleration, it incorporates a GPU memory-centric runtime featuring GPU-side pooling, streaming mini-batches, and overlapped offloading. This design enables much larger configuration spaces and shifts the bottleneck from host-side limitations back to on-device inference. Our evaluation demonstrates that our work fundamentally expands the scale of solvable problems. On an NVIDIA A100 cluster with 64 GPUs, our work achieves up to 2.32X end-to-end speedup over the highly-optimized NNQS-SCI baseline while preserving the same chemical accuracy. Furthermore, it demonstrates excellent distributed performance, maintaining over 90% parallel efficiency in strong scaling tests.