... my question would be how do you put all of this together? Are you modeling price or its reaction to changes of these inputs? Both? ...
Let's suppose you could use the fundamental inputs to develop a price model for NG. Your model is developed over historical data, where all the fundamental values are know. Sounds like something that can be done with sufficient data and good regression package or programming skills.
You would still need accurate forecasts of these fundamental variables to calculate a future price. Where will you get accurate forecasts for weather, storage, and distribution disruptions? That's where these fundamental models become challenging.
