>So you have the question of why I can only directly perceive that emergent property in exactly one brain and not others
You are the thing carrying around that brain and sense organs, and the plumbing thereof. This is a unique situation, hence the uniqueness.
> Likewise you'd have to explain why the emergent property is apparently continuous through my whole lifetime over which my brain changes enormously.
Emergent phenomenon can be very robust, such as Jupiter's spot which was observed 340 years ago, or the common orbital plane of the solar system, which is billions of years old.
Also, your consciousness is not continuous. You turn (at least some of) it off when you go to sleep. Very curious! It's at least robustly bistable!
> Finally you'd have to deal with the hypothetical case where I am duplicated molecule for molecule and then ask which consciousness would I have direct access to, the duplicate or the original.
This seems very simple too. There are two copies of you at the instant of duplication, which diverge from that moment on. You1 would have access to the consciousness of You1's nervous system and You2 that created by You2's nervous system. This question is only difficult if you insist on something other than the bodies being involved.