Yes, it is easier to do that with a controller.
I had it with the physic tank in unity.
I would not do up and down shift for the tracks… just keep it simple.
In unity we used an xbox controller and the left and right trigger where foreward for the tracks… and the left and right bumper where reverse for the tracks.
Was actually pretty fun way of driving 
I don’t know how ww2 tanks did this is real life… I believe like you said the left and right lever where just a brake… so you steered by just slamming the brake on one of the tracks.