The 737-300 and -400 were perfect for the BNEHIR run.
The -200, hardly. Air Nauru did that for a couple of decades using NOU to be able to maximise loads. Very expensive if loads not there.
The Solomon's may do what the Norfolk Islanders did and opt for OzJet to do their service. The Norfolks lost out big time on that one in more ways than one with OzJet being the only winner, and only just.
A deal with the Vanuatuans can't be at all efficient for the Solomon Islanders. How can you possibly not get penalised in seat/mile costs if you have to fly from HIR to BNE via Vila? The paying Solomon's public will grimace at that thought. Wantok to wantok relations (Melanesian Spearhead group) should not come at a penalty for one party and benefit to the other.
The solution comes back to what we've hammered again and again. Partnership with the Nauruans. Is this solution to be avoided at all cost? If so, why? And how could that be rectified?
A few simple probing questions may go a long way in solving this dilema.