My game is miles away from yours but when I was at my lowest handicap, 13, it was almost entirely due to my short game and putting. Having said that, I still think a lot of it stems from driving. If I keep putting myself in poor positions it's almost like starting with a penalty stroke. If I am in an adjacent fairway, I will struggle getting back into position, especially if there are trees in the way, whereas someone at your level has the ability to get back into position easier and may salvage par or bogey at worst where I often end up with a double.