I'm playing it now. It's interesting and it has many different chacarters, I still didn't see all characters and those are the ones I could type:
-Makoto I think is EII-Fi "...Makoto is respected by many people as the Ultimate Hope, though he himself is very humble and even a bit embarrased of the title. In Danganronpa/Zero, it's mentioned that he has incredible strength inside, despite often appearing weaker on the outside. During hard times, he is shown to have the power to give hope for other people and affect their way of thinking. However, this is not always the case, as some people refuse to listen to him or simply do not accept his ideals." and there is more about him
here.
Kyoko is probably SLI-Te. She is very calm and objective and she helps Makoto with solving the class trials and she had difficutly getting close to other characters.
I agree with you on Aoi, ESE.
Byakuya I think is LSI-Se.
Monukama, hmm maybe LIE, but I also can see EIE. I think Beta>Gamma.
Toko - ILI. She is Gamma.
Celestia - EIE-Ni.
Yasuhiro - Maybe ILE.
Sayaka - I wasn't sure about her type except for being "ethical" but IEI seems to fit.
Kiyotaka - ESI-Se. His name "The Ultimate Moral Compass" fits with his socionics type.
Sakura - LSE.
Leon - SEE-Se.
Mondo - SLI-Si.