Although there are operators that service tarawa/funafuti/majuro internationally , I am not aware of any existing domestic charter or rpt service within the kiribas island group.
last i heard of air kiribati was that they had wet leased an ATR42 from a french company but i have not seen this aircraft for some time.
your options may be -
1. try to convince someone with a private aircraft in the marshalls (majuro) to run you down there for a wad of cash and a crate of rum.
2. there is always constant US military activity from Majuro to ALL the outer islands and seeing as this is an MIT project you might do well to get on the phone to the right people (polititians/government officials etc ) to organise military assistance for a patriotic cause . I would have some administration senior call the local base comander on majuro and have a polite (grovel , bribe etc ) conversation about thumbing a ride.
3. take a boat.