At a high level, I agree with what everyone else has said. But if I were standing in the boat coaching you, I would address your specific issue with a focus on your shoulders.
Your shoulders are leaned toward the boat essentially all the time. In this configuration, you'd need impossible tricep and core strength to hold the handle down to your hip.
Instead, you want your shoulders to go as far away from the boat as possible. In order for this to happen, your arms will have be straight (think about how any bend will just pull your shoulders closer to the boat), and your hips will have to go toward the boat (again if the hips come away that means rotating your shoulders more toward the boat). This means that improving where your shoulders go will magically repair these other issues.
You want to have the feeling that you're hanging your entire upper body off the end of the rope.
When you watch the best slalomers, you'll see surprising variation in exactly what they do with their knee bend and exactly where the rope handle is relative to their body. But if you look from hips to shoulders, all of them have their shoulders way away from the boat such that their upper body is basically in a straight line with the rope. Even more interesting is how much they stay with that as they ride the handle out. The upper body stays broadly in line with the rope even as the edge begins to change underneath, creating the so-called Reverse-C position for a moment. THIS is what results in the handle remaining close to the hips. In most other positions, it would require impossible strength to force the handle there.