Your handicap is much better than mine so you might not listen to me but putting is really my only strong point. On days that I don't actually play I practice putting for at least an hour. The practice green at our driving range has 9 holes-- I alternate between 1 to 9, 9 to 1, and putting to the hole opposite whichever I choose. If I three putt I start over from the very beginning (if I start on hole 1 and make it to hole 9 and then 3 putt I start over from hole 1). I also only use one golf ball because I feel that it really makes me focus on making the putt count. I got par on 5 out of 9 holes today and every single par was a one putt so it can't hurt.
Actually. My back gets pretty sore from putting so much.
Good luck out there!