That's an excellent synopsis and that theory is as good as any. What I can't reconcile about this version though is Shanann was clearly extremely frightened by MP on that night and - real or not - thought he was going to murder her. So how did Hackett & Pak come to meet and how did Pak get Shanann in his car?
I still think if MP is involved, it's most likely because Shanann ran away from him for whatever reason and went into the marshland to hide or take a shortcut and had an accident since she was under the influence and drowned.
Since this all happened so close to Hackett's home, I think he wanted attention so he contacted Mari and concocted the story. I think you're right in that he didn't know she was missing when he was doing this so then when he found out she was and eventually found dead, he backtracked hard out of fear.
In the January 10, 2016 statement of Joe Scalise of he states that on the morning of May 1, 2010 "he [Thomas Canning] meets up with Peter Hackett and he [Thomas Canning] and Peter meet up with Shannan."
This meeting would presumably be in the vicinity of Peter Hackett's residence at 47 Larboard Court, shortly after Shannan leaves Barbara Brennan's residence continuing her desperate search for help from any of the residences of Oak Beach. If Michael Pak had followed the route Shannan had taken down Anchor Way he very well could have caught up to Shannan after she left Barbara Brennan's property, and arrived in time to see Peter Hackett and Thomas Canning interacting with Shannan.
At this point Michael Pak tells them that he knows Shannan, and explains
his version of events to them. Peter Hackett offers medical assistance and administers a sedative to Shannan in his home for wayward girls. He "discharges" a sedated Shannan into Michael Pak's custody where she is then assisted into his car, and they begin the trip back to Manhattan. Shortly after Shannan becomes unresponsive in Michael Pak's car, and as previously stated Michael Pak dumps Shannan into the marsh off the shoulder of Ocean Parkway, and leaves her belongings in the vicinity of Peter Hackett's yard (in the event Shannan is discovered this will point the blame toward Peter Hackett). A sedated Shannan would have been powerless to stop any of this from happening.
There is too much circumstantial evidence to believe that Peter Hackett was simply inserting himself into the situation to gain attention, and that he had no contact with Shannan.
In the May 28, 2014 transcript of Mari Gilbert she states on page 98, lines 5-13, "I received a call from a man who said his name was Dr. Peter Hackett. He ran a halfway house, uh, place for wayward girls and that Shannan was there, he was taking care of her. And her driver, a guy came by the name of Pak to picker her up, he promised to bring her back and, um, she's not back and he's worried about her. Um, he's trying to help her. And nobody knows where Shannan is."
In the September 24, 2014 sworn affidavit of Bruce Anderson of he states that "in or about the winter of 2011 Dr. Hackett personally told me that he ran a home for wayward girls; that he had taken Shannan Gilbert into his home in May 2010; that he had treated her with medication that he had administered to her; that she was confused, and had left his home, never to return."
Evelyn Scalise says in her statement that she "heard Peter Hackett tell Marianne Conti that he was thinking about opening a clinic for drug addicted, wayward girls and prostitutes."
Peter Hackett stopped himself while answering Erin Moriarty of 48 hours' question about him calling Mari Gilbert. Peter Hackett is then quoted as saying, “Yeah, I'm sure I did. When you give … look let me not get into it.”
I don't believe that Peter Hackett murdered Shannan or had any intent to cause her death. To the contrary I believe he was really trying to help her, and that he was duped by Michael Pak.