Large language model (LLM) hidden widths—such as the 18 944-dimensional intermediate layer of the Qwen family—are often burst-aligned but not tile-compatible with heterogeneous NPU Cube engines, forcing the compiler to emit a small residual kernel that stalls the pipeline for up to 77% of cycles. Manual tuning does not scale across the growing space of model dimensions, sequence lengths, and operator variants. We present GenTile, a dual-role Research–Development (R&D) agent framework that closes the loop between LLM causal reasoning and on-device telemetry: a Research agent diagnoses bottlenecks from structured profiles, a Development agent materializes hardware-legal descriptors from compiler feedback, and iteration traces accumulate into a reusable knowledge base under an air-gap sandbox. On Ascend 910B, an offline hardware-faithful sandbox loop first demonstrates convergence mechanics; on real pretrained weights, the loop then measures the full multi-objective trade-off—latency, energy, memory, AICore efficiency, and approximation error (ε)—across six projection families from two Qwen generations (Qwen3.5-32B and Qwen2.5-7B). From telemetry alone, the agent deploys lossless sibling-projection fusions (QKV, gate–up) consistent with production inference-engine layouts (1.06–1.16× faster, up to 13% lower energy, ε=0, stable across sequence lengths, layer depths, and both models), and rejects every lossy low-rank rewrite—including a 1.39× lm_head speedup whose measured ε=0.89 exceeds any usable accuracy budget—while validating the Eckart–Young cliff prediction (ε → 0.002 at the tail rank) on structural layers. Baselines, ablations, cross-dimension generalization, and a sandbox loop that matches the geometric Oracle within four generations without exhaustive search further support the framework.