My technique doesn't require a lot of flexibility or strength. It does require timing.
Stand facing the cowl with your right fingertips on the prop, and your left hand holding the doorframe.
Flip the prop, and as the engine fires, jump toward the rear of the plane, twisting your torso toward the front of the plane as you do so.
Simultaneously, while still in the air, pull yourself aftward with your left hand on the door frame, transfer your right hand to the overhead diagonal in the cabin, move your left hand to the far side of the rear seat bottom, and use your hands to help rotate your body to align with the seat. Your hands don't carry your weight, they just assist in rotating your body. You don't touch the door sill either - your butt clears it and landing in the rear seat, it is the first thing to touch. If you are solo, leave your left knee extended and bring your left leg in over the top of the front seat. If you have a passenger, bend your left knee and bring your lower left leg across between the stick and the back of the front seat. In two seconds from prop flip, you are sitting in the back seat with your feet on the brakes, strapping yourself in. In 50+ years of flying J3s, I have never found a faster, easier way to enter one.