What I'm saying is that 4 years in TKD should result in you beating 1.5 years of boxing pretty regularly in sparring. If it doesn't that means there's an issue in your TKD sparring.I don't know what that means.
Sigh.. It's not my invention to hook off the jab. I don't believe you boxed either. I specifically requested guys who have boxed for a long time in the OP
You're right..it's not your invention to hook off the jab. But it is to hook in the way that you're describing it. I did box for 4-5 years. That's outside of my other 19 years of training in various arts (23 if you include the boxing). But what you're describing sounds like a waste of effort, and wouldn't impact anyone with serious training/experience in boxing. Unless I'm misunderstanding it but for some reason you've ignored every request to provide a video of what you're explaining so I can't know if I'm understanding you right.
If you provide that video, I'll be happy to discuss it. Until then, I can't picture any way that turning a jab into a hook at the last second would be helpful to the puncher.