I am probably going to get flamed for this, but here goes anyway! I would recommend you try a HIGHER gear and a LOWER cadence when you notice your heart rate going up. You are "blowing up", going anaerobic; keep going and there are three possible outcomes: 1) you stop 2) you pass out, or 3) you reach the top before 1 or 2 happens. If your knees and quads will take it, this may well help. High cadence/low gear stresses your cardiorespiratory fitness, low cadence/high gear stresses your musculoskeletal system. On a long climb, you can switch back and forth, and even stand for a while.