Controller suggestions

I need to move a player controlled unit through the world and not have it go through the static scene. The problem is the unit sorta hovers above the ground and has an unusual shape,‘T’ shaped, sorta like a plane. Its longer then it is wide and rotates. If I use a capsule or box, then the nose would stick out of the controller shape and penetrate the walls.
I was thinking of using a capsule, with Z up, oriented length wise, but then when it turns the capsule wont align with the model. I might be able to rotate the character controller capsule by accessing the controllers->actor->shape (capsule or box) local pose rotation, but Im not sure if this would work because Im not sure if physX will reset the local rotation.
What would be the best solution to enclose and detect collisions for a unusually shaped player controlled character unit?

You might want to select a capsule or box CCT that best fits the entire model, then use PxController::setUpDirection to rotate the CCT up direction.