The XII team was the old Product Development Division 4 assigned to Yasumi Matsuno; Executive Producer Akitoshi Kawazu stepped in during the last year of development to mediate between the feuding factions and guide the project to completion.
It was disbanded upon the initial Japanese release with people going everywhere - quite a number were rolled into The Last Remnant (Kazutoyo Maehiro, etc.), some took up key positions in the new R&D department (Taku Murata, Hiroshi Minagawa, Takeo Suzuki) that would develop Crystal Tools, some started up work on FFT A2 (Yuichi Murasawa, Ryoma Ito, Kyoko Kitahara, Jiro Mifune, technically Yoshida/Minagawa as well in an artwork quality control capacity), some already left development during the shakeup (Akihiko Yoshida to Hiromichi Tanaka's department, Hideo Minaba to his own independent company), some dispersed to FFXIII or FFvsXIII (Akiyama moved to FFXIV 1.0 at some point).
These were all Matsuno loyalists (to the point that Hiroshi Minagawa actually led the teams in practice even if he didn't receive credit as project leader; not surprisingly, the section leadership assignments were stacked in favor of Matsuno's people), so I'd be somewhat surprised if they wanted to work with Hiroyuki Ito again. Matsuno remains legendary, and the staff frequently rally around the three main figures to extend/protect the legacy. There's a fascinating story to be told somewhere, and it's fair to say that they aren't your typical game developers.
For his part, Ito eventually got what he wanted from FFXII (added the License Board; produced/directed the International Zodiac Job System version to his own liking, which supposedly resurrected an original design concept that had been scrapped early on), which was to create his game system on his own terms, which is traditional Square Enix policy. Even in interviews, he mentioned that gameplay system was his main concern, with story, art, and the like being less important to him.
Way too much false speculation been passed off as fact in your post.
Akitoshi Kawazu never took over FFXII to split up feuding factions. He was merely there to provide motivation for the remaining staff once Matsuno left. The team's morale had obviously fallen because they had lost their leader, so he stepped in to provide encouragement and counselling. He has even gone on record to say that Ito and Minagawa were doing a great job as directors so he never really had to get involved with the project deeply. Instead, he just supervised and provided encouragement to the staff.
GameSpot: Was it difficult to take over a project partway through?
Akitoshi Kawazu: Yeah, it definitely was difficult. While it's not at all unusual to help out on a number of different projects, to come in at a producer-level role and oversee things was definitely something that was hard to do. That having been said, the original directors that were there from the beginning of the game, Ito-san and Minagawa-san, did a great job and since I only had to oversee the general flow of the project, and they were there doing such a wonderful job--that did make my job a lot easier.
http://www.gamespot.com/articles/qanda-final-fantasy-xii-producer-akitoshi-kawazu/1100-6160463/
"To begin with, Matsuno-san and I are very much both game creators - to step in halfway through a project that someone else has started and expect to be able to finish that in the exact same way that they had planned, is not something that is necessarily completely realistic," he explained when we met him in London last week.
"But then, I wasn't necessarily doing the same thing that Matsuno-san had been doing up to that point. My primary goal at the time was to see the project through to completion, and to give encouragement and support to all of the members of the staff that were still there."
http://www.eurogamer.net/articles/i_finalfantasyxii_ps2
Secondly, the belief that the FFXII team has been disbanded is incorrect. I used to believe it, but recent evidence indicates that they only split up temporarily to work on other projects. We've already seen core members reunite for Tactics Ogre. When it comes to AAA projects, we'll only know if they've truly reunited when we see the core staff for whatever Ito is working on. If it includes many FFXII staff in important roles, that would confirm the FFXII team was only split up temporarily and have now reunited for Ito's project. To add to this, Kitase already confirmed in February 2014 that a FFXII HD Remaster being made depends on if the team that made FFXII wants to make it and that he hasn't heard any plans for them doing so. This alone confirms the FFXII team, or remnants of them, still exist within Square Enix. This also corroborates with Kitase telling me at the LR FFXIII European launch that Hiroyuki Ito has his own development team.
FFTA2 was in development before FFXII was finished, but it was being worked on at a glacial pace while the team were trying to get FFXII out the door. It's only when FFXII finally went gold that development finally ramped up. The game didn't start development when FFXII finished, as you claim.
With regards to the staff being Yasumi Matsuno loyalists, that's no longer the case, as the man is gone. He no longer works for Square Enix. He's passed the torch to Minagawa and Ito, so any staff that really cared about Matsuno would support whatever projects those two want to get off the ground. We've seen this already with Tactics Ogre. Many of the Matsuno faithful reunited under Minagawa to make the game. Even Matsuno himself returned to support Minagawa's project. The same can also happen with whatever Ito's working on, but until the game's announced and we see the core staff, we'll never know for sure. However, the fact Matsuno chose Hideo Minaba to be Art Director/Character Designer for Crimson Shroud, even when he'd only worked for him for three games prior to that (FFT, FFTA, FFXII), is strong indicator that he has a lot of respect for Square staff that joined him on FFT.
Out of all areas that make up a video game, Matsuno believes the game design is the most important. That being the case, Ito was the game designer of two of Matsuno's games and even co-directed one of them before Matsuno stepped down. Those two games are of course FFT and FFXII. Therefore, taking this into account, Matsuno must obviously respect Ito. If Ito ever made another game (he hasn't directed a game since FFXII) and wanted Matsuno to be involved, it's very, very, very, very unlikely Matsuno would say refuse. It's just not customary in Japan, especially given their project history together. It's made even more unlikely by the fact that he agreed when Minagawa asked him to work on Tactics Ogre.
Lastly, it's not confirmed that Ito didn't want to add or change any story elements to FFXII IZJS. On contrary, what is confirmed is that he wanted to add even more changes to the game, but couldn't due to not having enough staff. Some of these changes could have been scenario/side-quest related. After all, Ito was heavily involved in structuring and pacing the narrative of FFIX, so it's unlikely that he would completely ignore the chance to add to or edit the scenario/side-quests in FFXII IZJS if he had the opportunity.
Hiroyuki Ito just mainly cares about game design over story, but that doesn't mean he refuses to get involved in the story if nobody else is available to work on it. He just prefers that if there's people available to work on the story, he'll leave them to do that and instead focus his attention on the game design. On the
FFXII IZJS official website, he role-played as an aristocratic citizen of Ivalice and made a diary of the game's development leading up to release. It was a great read and full of fourth-wall breaking humor. Regrettably, it's completely illegible now. However, somebody who didn't care about story whatsoever, would never think to write so creatively just to update users about the state of the game's development.