There are bound to be more than two health insurers in Hawaii. Try googling "health insurance Hawaii" and see what you get.

It may be pretty expensive, but you could look into expat health insurance, at least in the interim - six months or so until you can claim Hawaiian residence. Depending on the type of work you do, there may be health insurance available through a professional society or association connected with your profession.

Or, you can just find an independent insurance agent in the phone book and go in and ask about health insurance plans you might be eligible for in your circumstances. (Or better yet, go talk to a couple of independent agents and see who comes up with the better deal.)

Coming from a single source system (like Canada) the US system must seem like a real jungle. (Actually, it is!) You have to be kind of aggressive about going out and finding the various options, and you may wind up having to pay big premiums or living with exemption periods if there are pre-existing conditions to deal with. But there are always multiple options.
Cheers,
Bev