In my opinion, GIR's are the single most important stat to lowering your score. At least that has been my experience. Granted, GIR's can be traced back to other stats such as fairways hit (which you are doing fairly well on), so it's likely that if you have a high GIR percentage then you are doing multiple things right. However, if you give yourself two putts to make par it will significantly lower your score. It doesn't matter if you are barely on the green and have a 40 footer, just give yourself two putts. Forget the flag placement and always go for the middle of the green, giving yourself the most room for error. Brace yourself to see your average putts per hole go up because they will. You are going to 3 putt some and that's okay, but every once in a while you will knock one close for a birdie or sink a 20 footer for that one putt. Regardless, a GIR significantly increases your chances to make par, and essentially limits your worst case to a bogey.
If you can strive to double that GIR percentage, you essentially are giving yourself 6 pars per round. Maybe you blow one with a 3 putt or maybe you knock down a birdie, but it will average out close to 6 pars per round. Then based on your current scrambling percentage, you will pick up another 2 pars from the remaining 12 holes. If you can play the remaining 10 holes at just a +1 average, you end up around a 10 handicap... I know it's easier to type it out here online than it is to execute on the course, but it allows you to see how important hitting those GIR's are. Just hitting 1 out of every 3 greens will gain you three strokes per round and get you near that 12 handicap that you are striving for.