I have a similar issue. My most recent round I drove the ball better than ever, straight, where I was aiming about 250-270. My ordinary drive is probably 240, but I am using new driver for me and hit fits me and I have gained distance and accuracy. Then, being beitween 70 and 120 out, I completely fell apart. I am a 12 and getting close to or on the green in two even with an off center drive is fairly easy. It all came down to chipping and putting. On this day, I couldn't hit a green from 70 which is lousy and frustrating and compounded throughout the round.
But, that said, I believe that chipping and long putts are the problem. Even the pros spray a drive and mishit an approach, but their ability to chip and make putts from 15 feet in sets them apart. For me, my inability to take a 10-30 yard chip and put it within 15 feet is crushing mentally and adds 5-10 strokes to my score. Also, say I hit the green, but have 30-50 feet to deal with, hitting a good lag to within 6 feet is rare. Often I am short, long, or just don't read the break right over the distance of the putt. I just have to be better getting closer to the hole. Shorter putts and good chips breed confidence and create good memories to rely on.
Also, if you note it, when you are in a chipping situation, there are more variables to your shot selection and swing type than anywhere else on the course. You are trying to repeat one swing with a putter, driver, and iron. When chipping you can bump and run with different clubs, hit a soft chip, use a putting swing, have to hit down in the rough, hit from the sand, a flop shot, choose what degree wedge to hit, control backswing for distance, have a short side pin, a lot of green to work with, and then you have to make solid contact. I often make the wrong decision for the situation I am in and it adds a stroke or two per hole.
I have practiced on chip and run and soft flip (not flop) shots and improved. Recently I started practicing using a putting stroke with a hybrid to run it up or out of the rough because it moves through the rough better and if I can control the distance then I may be able to closer on a hole without a big lip to deal with. I don't think I will improve my handicap much until I am able to execute 5 or 6 different shots around the green with a decent degree of proficiency.