The rapid proliferation of Large Language Models (LLMs) is increasing electricity demand from data centers, creating new challenges for power-demand forecasting and grid planning. A key difficulty is that architecture- and deployment-related information that affects inference load is often private to LLM providers. This paper proposes a two-stage, mechanism-assisted forecasting framework under information asymmetry. In the first stage, a stylized incentive mechanism elicits verifiable reduced-form demand parameters from LLM providers at a chosen reporting precision. In the second stage, the elicited parameters are incorporated into forecasting models as architecture- and deployment-informed features. Using calibrated synthetic scenarios constructed from public data-center energy reports, open LLM-inference energy benchmarks, and secondary public estimates, we find that incorporating elicited parameters reduces the mean squared error (MSE) of the ResNet forecasting backbone by 65.1% relative to an architecture-agnostic ResNet baseline. Similar improvements are observed for a gradient-boosting model, indicating that the main empirical value comes from procuring informative provider-side demand features rather than from a specific neural architecture. The results should be interpreted as a proof-of-concept demonstration rather than a full operational model of LLM serving or power-system dispatch.