it is better to make it by phone anyway, you can ask to book a ticket and maybe pay for it at the airport counter at check in, some airlines still do that.
i heard the new airline is nice, offering very cheap flights between the islands, i dont know why you say it is a gamble- its not a charter airline.
by the way, whenever you call the airline, make sure you take the name of the person you talked to and his/her`s ID number, so if anything goes wrong, you have a name as a proof.

you can call them up and speak to a customer service agent, they can help you out with it, by the way, there is a new airline in hawaii that fly for cheap between the islands- the name is go airlines