If the ride vehicle isn't the Ford Angelia, than what even is the point of the ride?
Have a detailed queue through a cave of the forest, featuring lots of animatronic creatures. Towards the end, a projection of Hagrid explains that the car was enchanted to take guests on a tour of the forest. Board the car, brief dark ride scene going past some centaurs and Grawp, than blast for a 2 minute long coaster section, winding low to the ground, through the terrain and trees, with the occasional animatronic of a magical creature on the side. Maybe one show-scene in the middle, Big Thunder Mountain Railroad style.
Just make sure there's a looooooooooot of trees and plantlife so it feels like an actual forest, and blocks most of the bare steel coaster track from view in Hogsmeade, and we're good.