STAR TREK II is obviously considered one of the greats of STAR TREK, so of course the writers of STID looked to that to do their own spin on it. That seems to be the case with most remakes/re-imaginings/rebootquels,ect. Most things successful in the first place will get that kind of attention, but rarely anything that was considered a failure. For example, maybe there's a bad film out there that you want to remake yourself, because you see the potential in it and know ways in how to improve it greatly. Studios would just laugh at you and say they're only interested in remaking movies that were successful, because of brand recognition. I guess remaking STAR TREK V: THE FINAL FRONTIER will never happen, because I have ideas for that. If we're to continue with STID's idea of looking back at older stuff and giving it a new spin rather than do something entirely original, then here's my proposal.
If I had the creative powers I would actually look back at TFF and take a couple of elements that worked and even some that didn't. This is my own premise:
Sybok's background is for the most part the same. A renegade Vulcan who was banished from his homeworld for promoting his ideas that went against the teachings of Surak. He looks to emotion as self-knowledge. The finding God angle would be dropped. I would still cast Sybok with a very charismatic actor because that to me is one of the most vital aspects of the character. Laurence Luckinbill was one of the best castings in that film and was very believable as a man who would leave a movement with the charisma he carried. My story would basically pick up on a thread that began on the 2009 film with the destruction of Vulcan. After Nero's destruction, a great number of Vulcans had a very difficult time recovering from the trauma, that their logical upbringing isn't helping them suppress the boiling emotions within. Many of them are all emotionally lost, some committing suicide, being sent to mental facilities, ect.
Enter Sybok. He blames the teachings of Surak for not preparing the Vulcans for the trauma they went through and decides to take a great number of them under his wing to help guide them emotionally. Using logic and emotion, he gives them all a focus: Romulus. Despite the Romulan government denying Nero had nothing to do with them, Sybok believes it was a lie and that Nero was secretly working for them to destroy Vulcan and the Federation. With this propaganda, he is building up his followers into becoming his own soldiers to fight the Romulans as a way for avenging the homeworld that was destroyed, and believing that if they take down the Romulans that their quadrant of the galaxy would be saved from further destruction. That is what Sybok labels as true logic, and with the Vulcans being emotional they begin to believe in that flawed logic, making them more determined and dangerous. The movie begins with Romulan colonies being attacked by Sybok's terrorists.
Back at Starfleet, Kirk and Spock are called into a briefing with an admiral. The admiral informs them that the Romulan government asked for assistance in capturing Sybok and his followers. If the Federation does not take any action on the renegade Vulcans, the Romulans will believe that they are actually condoning Sybok's attacks thus regard it as an act of war. Kirk is given carte blanche to capture Sybok dead or alive to avert the first war with Romulans in a hundred years. Through this film, Spock comes to truly realize the importance of Surak's teachings, that when Vulcans are driven by emotion they become more unstable than most species and are very destructive. That is why the logical upbringing is most paramount for Vulcans. Kirk comes to respect Spock's logic more. This understanding strengthens their friendship.
When confronting Sybok, he defends his actions because he not only believes in his conspiracies but that he also gave these emotionally lost Vulcans a purpose and goal to strive for. He admits to not liking the killing, but believes that it is the logical thing to do to not only ensure the safety of their quadrant but also give the emotionally scarred Vulcans some closure whether it's through dying for what they believe in or succeeding. Despite his leadership, many of the Vulcans begin to question whether Sybok should lead them. Spock uses this as an example of why emotions cloud the judgement of Vulcans. Even though Sybok has mastered his emotions, not all his followers have that capacity and will eventually turn against him as their emotions supersede logic.
I think this would make a good entry for the new crew with Pine and Quinto. The idea of logic vs emotion, finding the balance is very Roddenberry and with the right talent I think it could make a very good story that both compliments both the original Star Trek and the direction the current series is trying to take.