As @Horton said in the thread you mentioned, the number 1 priority for your level is how you stand on the ski at all times. If I were you, I wouldn't worry about your turns right now. They look fine and your position as you cut through the wakes is what needs focus.
Onside (going from passenger's side to driver's side):
What's good is that you're cutting all the way through the wake and changing edges at a pretty good spot
What you need to work on is getting into a stacked, standing position. Right now, as you cut into the wakes you are bent at the waist, with your hips trailing behind the rest of your body, and there's quite a bit of distance between your hips and your handle. What you want to work on is moving your hips "up" or "forward" so that they're close to the handle. The goal is to have your ankles, hips, and shoulders all in a single line on top of the ski. So if you imagine a rod sticking straight out of the top of your ski, it should go right through your whole body. Right now, it would go through your ankles and shoulders but your hips would be behind it. As you know, @Horton likes to coach this by telling the skier to stand up taller on the ski. This should naturally bring your hips up in between your ankles and shoulders. More traditionally, this was coached by having the skier try to get their hips closer to the handle while they're in the pulling position (while keeping your arms out straight). Maybe try both to see what's more effective for you.
Offside:
On the toeside you are standing up and stopping your cut before the wakes, and then resuming it after having crossed them
Your goal should be the same as on your onside; specifically, you want to cut all the way through the wakes on edge and then come off your edge right after
To accomplish this you'll need to get into a stacked position on this side as well. The good news is that you'll want to work on the same thing as on the onside - establishing a tall, "stacked" standing position on top of the ski by getting your hips to stop trailing your ankles and shoulders, and maintaining that position all the way through the wakes. It'll probably be harder on this side, but think about your sternum and hips facing the same direction as the ski tip, stand tall and make sure your hips are forward. Basically, as you cut your arms will be out straight, but with your hips forward they should end up running down your torso, so that your handle is near your hips in a position that's both efficient for taking load from the boat and for riding on top of your ski.
Note: You're probably fine at 15' but if you start working on this and run into issues where you crash and/or start to get scared of the wake, you could try 28' off or 32' off to see if it gets easier to deal with.