I would definitely put something on the bottom, if you have any of your fabric strips left over I would pick 3 or 4 or however many it takes to make it a length you like and run them perpendicular to the body of the jacket and simply line them with a solid piece of one of your fabrics. This will give the jacket a nice finish and if you think the banding needs more body simply put a piece of light weight batting in and SID on the added piece.