Battery drains when phone is turned off
This is not a definitive answer but most likely cause IMO based on my experience with a Note 2 exhibiting similar symptoms. 

You did a thorough job of investigating the causes and this pretty much rules out wakelock as the common culprit in such cases.

That leaves with one possibility - hardware. Something in the hardware is causing electrical drain. This needs to be investigated by competent people. In my case, it was rainwater seeping through ear phone port that corroded the motherboard. Cleaning with alcohol and drying reduced the drain but not significantly as the corrosion was deep.

The cost of investigating and replacing hardware is significant and in your case, you are not the first owner, so it may not be worth it. My suggestion would be to use it as it is for as long as you can.