I completely agree with Cheung.
My advice for you to remember: you do not need to worry about all the details and everything that is wrong, just try to take the shuttle earlier. This will result in a better contact point in front of you. Regarding the contact point over your head - stop worrying about it. The fact you let the shuttle drop is a huge sap for power, and will result in all kinds of "problems". None of them are actually problems, they are symptoms of a single problem: late contact point. It is really that simple! For now, stick to taking it in front of you when practising. All you need to do is get comfortable taking the shuttle earlier. This could take up to 6 months - thats ok! But if you video yourself every week, you will quickly see the differences
A word of warning too... try to stop analysing and reviewing your badminton for a bit. Just focus on broadly what you want e.g. reach up more, and more and more! That may help prevent you over complicating all this technique stuff

You have a great foundation, now just finish it off!
And try not to fool yourself into thinking racket technique changes are "harder" than others - the moment you accept them as being easy, but will take time, then the pressure is gone. Just focus on what you want to do, and persevere even though the first 2 or 3 sessions could feel bad. It won't instantly feel great for most people -
but you have to keep going in spite of that.
Here are some tips for learning to take the shuttles earlier:
1. If, as the shuttle is coming, you feel you could physically reach it now, then you are too late with your swing. You should have already hit it.
2. Aim to hit the shuttle 1 metre higher than you currently are. It doesn't matter if you succeed in taking it that much higher - its just a cue to help you break your own barriers. Even once you have succeeded in taking the shuttle higher, repeat the exercise again. See if you can get it even higher again!
3. Learn this with clears and half smashes. Full smashes will probably hinder your learning, but don't be surprised when the half smashes become a lot more powerful than you are used to.
4. I believe your contact point could be as much as 1 metre in front of the body i.e. if left to fall vertically it would be 1 metre in front of where you stand - that's how much you have to reach for the shuttle!!!
5. Finally, it may be wrong to obsess with the "height" of your contact, but the concern is more the "lateness" of your contact. Aim to reach as far as you possibly can to play the shot - but this doesn't always translate into reach for more height - it could be reaching further in front or to the side etc. You want to take the shuttle at full reach! Currently, you are bending your arm.
Please remember: the above are coaching cues only: they may or may not represent how you will optimally hit the shuttle - they are just ways of you experimenting with your boundaries.
Good luck!