I hate to say it - but I was struck by the impulsiveness of Harry's actions, compared to his history that you've established so far. I can see Hui pushing him in that direction, but honestly, I can't see Harry going along with it.
1) Harry came from a period of WAR. While admitted, he didn't see Sirius end up falling through the Death Veil, he has seen Cedric killed, and suffered through the rebirth ceremony. He's found a group of adults that actually respect his abilities, and are willing to listen when he tells them things need to be done, and what needs doing.
2) He's got warning that triggering the symbol will take him to confront Voldemort. Voldemort has been contained so far - no reason what so ever to expect a few days or even a few years is going to make that much of a difference.
3) He's just been re-assigned on a rather irregular set of orders to work with Admiral Kirk on finding out more about his powers, finding out more about his community (which he is now back in contact with - which means a LOT of work integrating what they know into the general human corpus, as well as feeding the information HE knew that had been lost into both frameworks, and getting that integrated.
3) As well, there is checking with other races for possible information on Harry's abilities, and concentrated testing of the possible detection of the energies involved. However, it is somewhat surprising that Kirk was not somewhat adversely affected by the Gary Mitchell incident with respect to a human having magic powers, or Charlie X. In fact, that a human could have these kinds of abilities would not be that much of a surprise to Kirk, or to Starfleet in general, though it's quite possible that no-one who knows of their wizarding heritage happens to have clearance to know of these kinds of incidents. Harry's record to date, though, especially his being extremely circumspect about using his abilities, would have allayed his qualms.
4) Still, there's OBVIOUS approaches available for Harry to move forward in a much safer manner - properly investigating the Hogwarts/Hogsmeade area, investigating the Diagon Ally Memorial Park, thoroughly scanning the area around where Gringott's once was, investigating the possibility that human technology has advanced far enough not to be affected by magic (or at least, not as badly). Studying under Vulcan masters, who seem to have abilities quite similar to Legilimancy/Occlumancy, would be an easy realization. In the end, I would expect that after five or ten years, a carefully picked team of Starfleet officers, many selected from those with wizarding ancestry, would be stationed both in the park, as well as near Hogwarts/Hogsmeade, and several orbiting bases would be targeting the areas with close surveillance, while Harry, carrying a large set of supplies and tracking devices, set off the trigger in the park.
Still, that would not be this story, from what I can tell - and it might not be as exciting a story. Then again, since you've integrated the Battlestations/Dreadnaught plot line, I can see Harry and Hui being joined by Lt. Piper, with her crew causing some interesting problems...
("You bent the ship! How are you going to explain that to Commander Scott?" - even THEY knew who's ship it really was!)