The liveaboard Naia based in Fiji does go there very occasionally when it is chartered for scientific reasons. I asked them about going and I was contacted by the scientific group going who said they did have room for me. The cost was about $25k! Yes that is $25,000! It was for about three weeks as I recall but a huge chunk of that was at sea with two dives a day (if it was convenient but only if you did not get in the way of the scientists). There is a reason why the line islands are about the last place left on earth that is untouched by man, they are literally in the middle of no-where, you cannot get to them and when you are there, there is no safe anchorages either!
If you can find a way of getting there except by owning your own boat, let me know and I will be right there as well!