This is a good question as their are numerous factions. As far as I can tell, it seems to be between Liebel Groner (he's the believer in miracles), Yehuda Krinsky (the one with all the international contacts), some smaller groups and probably also the Schneersohn family as they control the rights to the "Tanya" the textbook which is the "Bible" of the Chabad group.
It's claimed that the "messianists" are a small group. But they're very vocal. A "Moshiach Bookstore" that was in Crown Heights went out of business, so it's possible that it's not all so bad but some people in this movement definitely went off the deep end.

If you look up Hadar Hatorah's web page, you'll see that Rabbi Shea Hecht, is the executive director and Rabbi Yaakov Goldberg is the Rosh Yeshiva. Goldberg was hand picked by the late Rebbe, Menachem Schneersohn. Hecht's father, JJ Hecht used to run (and I think he founded) the National Committee for the Furtherance of Jewish Education, which also operated out of the same building at 824 Eastern Parkway.
Who they're accountable to I'm not sure, but I've seen R. Krinsky around the office.