I would suggest working with single leg wall sits and holding the bottom position of the pistol for time. As they are isometrics, these moves should help build joint stability for these sticking points. The key is to ensure that your knee and hip are aligned properly.
For the wall sit, ensure that your knee is not tracking inward and that your femur more or less points forward from your hip. Try to press through your heel, you can even raise your toes and the ball of your foot off of the floor to make it more stimulating.
For the bottom of the pistol, ensure that your hips are squared with the floor, so that you’re level and not leaning one way or the other. The free leg should be straight ahead of you.
Work on holding those positions for time instead of doing pistols, and see how it affects your pain. This, combined with your more basic squats and lunges, should be plenty of leg work. If not, you can get more leg work by bridging. If you hold a bridge long enough, or do enough bridge push ups, your upper body will fatigue but you can actually keep going by using a sustained hip thrust combined with a leg extension to pull your body up with your lower body. In fact, this movement is the basis of the stand to stand bridge! I am hesitant to suggest something like jumping or running to you because of the pain you described with pistols.
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