It's best to separate parks, Tianmen Mountain, and transfer days. Starting early is important, but cramming the cable car and all the viewing platforms into one day usually detracts from the experience.
Let the weather decide the order
Fog and clouds can be part of the scenery, not a failure. Plans that depend most on weather can be decided the night before.
Respect the time for vertical movement
Queuing, cable cars, shuttle buses, and walking all accumulate. The route on the tourist map is very tight, but it can actually be quite physically demanding.