Naigani is more 2.5-3 star, and so probably falls off your list.
However we have great beaches and grounds. We dive E-6 and Wakaya Passage, which are two of the sites the Nai'a dives but those two sites are an hour ride as well as being pretty weather dependent. We have a multitude of dive sites that are 12 to 15 minutes from shore that are very very good. Today we dove Circus Circus. An older couple that have 600 dives over the past 35+ years (and just did 12 days diving Taveuni and Namena) said afterwards that it was one of the best dive sites they have ever done. They also stated that they had not expected to ever again see a dive site with the healthy soft corals and multitude and variety of marine life that they saw on this dive.
Our food is very good but not gourmet and the staff is VERY helpful. We are a smaller boutique dive op that caters to the wants/needs of the divers in house at the time.
The Pacific Harbour shark dive is very impressive and, if one doesnt have a particular objection to such things, it is well worth a quick stop in that area to do that once. For me, the other diving in Bega Lagoon is substandard by Fijian standards.
Taveuni and Namena are excellent. Namena can entail some long boat rides unless you stay at Moody's. I am told Moody's is on the higher end of the price scale but, having never stayed there, I am not sure exactly how much that is.
The Bligh waters have some of the best diving in Fiji but, again, for a land based operation you will most be looking at some longer (in the hour range) boat rides. Getting out to the Bligh waters is often a problem weather wise.
The Great Astrolabe reef is reputed to have some GREAT diving but, once again, getting outside the reef to experience it is very hit or miss depending on weather and swell at the time. I spent a week there once and the diving inside the reef was mundane. During that week we got outside the reef one time but it was in spite of the weather so that we could do the manta ray dive. The mantas were spectacular but without them the rest of the dive was average. Getting back on the boat was a pretty singular experience LOL.
As far as liveaboards, I have no personal experience. Friends, people I have dove with that had done the livaboards in the past, and exp-pats living in Fiji pretty much unanimously endorse the Nai'a. I am sure the others do a credible job as well but the Nai'a seems to be just a cut above.