I have a tendency to hit my irons heavy / fat due to a swing issue caused by a medical condition. I have only one eye (left) and play the ball very forward in my stance in order to see the back of the ball at address and when striking the ball. I am a very good driver of the ball , good fairway and hybrid player but I do struggle with my irons and chipping.
I was struggling this year very much like yourself as in hitting chips and short irons fat. I moved to a V sole in the Srixon Irons and though they help greatly in turf interactions the short game was still fat. The real cure was getting the right wrist cocked back in my initial movement away from the ball. It allowed me to strike downward into the ball curing the fats and really awakening my entire golf game. The fats were caused by an early release of my hands before striking the ball forcing the club into the turf before the ball. There are clubs to help with turf interaction but try a short game lesson first. It did amazing things for my game.