Rebreathers offer many advantages for diving beyond recreational depth; the most significant of which is probably a constant partial pressure for Oxygen (O2 percentage in normal breathing air starts to get toxic beyond certain depths); but the requirements to decompress remain. And in that regard, so do the dangers of decompression sickness. Given the remoteness of Niku, you would either have to avoid decompression obligations, or bring a recompression chamber (and doctor) along for safety.
The 600 foot depth of the Richie Anomaly, combined with the remoteness of the dive site and apparently rugged terrain, make for an extremely hazardous undertaking for divers--much better and safer options with manned/unmanned submersibles. Where I think divers could be helpful is the first 140-200 feet of depth along the "Bevington object-wire rope video-Richie Anomaly line" to look for debris. Again, depth and time conspire to incur decompression obligations even at relatively shallow depths. 165 feet for 20 minutes incurs 30 minutes of decompression for open circuit (normal SCUBA) or 21 minutes for a closed circuit (rebreather). Up to 130 feet of depth can be explored without decompression obligations but bottom time is very limited (as Scott pointed out). Of course, who knows what lies waiting for discovery in the first 100 feet, where bottom time is greater and risks far less numerous.