@MISkier I think you are brave for posting the video and seeking help. Brave is cool and helps in slalom.
You can correct this fast and easy. Don't think of it as changing/overcoming a bad habit. Think of it as learning a new one. Nobody is leaning against a loose rope. Most bring their hands in some (or a lot) at the finish at various times. However, once they make contact with the boat (line comes tight), arms are down/ straight.
Aside from the physics of centripetal acceleration as described by the Adams, allowing the boat to move ahead a bit at the turn in also creates a tighter line, a more secure line, a line you can lean against. Hearing it expressed different ways helps because one of them will make sense to you. I like the way "patience" is described in the video below. Make the turn, set the angle and wait, wait for the boat to take you across. Don't try to get moving across because if you do this too quickly you will create a loose line. Receive the load, don't create it. Now, you are the rock on the end of the string and you will zing. The audio isn't good in the video but you can make it out.
Treat yourself to some pro coaching. You'll love it and feel empowered and renewed. If you can free ski some, do the lean drill out beside the boat, see how far you can ride down the lake in that position with your arms straight. Next ride out, do the same drill with your arms pulled in; it's exhausting. So, if you can run buoys with your arms pulled in, you can damn sure run em with your arms straight cause it is so much easier.