Even if they could get supplies of iron and coal easily, the main question is "What good would it do?". Both Japan and California have their own industries, connected to large nations, with a large population and cadre of skilled workers. It costs money to haul iron and coal hundreds of miles across the Pacific, and even more yet to haul finished products someplace to sell. Moreover, you're talking about a nation with under 200,000 people, a good chunk being uneducated Asian plantation laborers with little attachment to the nation, and most of the natives being rural subsistence farmers and ranchers or field supervisors on the plantations. Not to mention you had a POD where you just decapitated the locus of the economy and caused many of the most educated and wealthy people in the islands to leave. Hardly the makings of a good situation.
In short, an independent Hawaii is going to be poor without focusing on cash crops. It's just too far away from everything, too small and too undeveloped to be the hub of industry. Hell, it's going to be poor even with cash crops. We didn't start really getting a healthy economy and development till tourism took off, and even then it was bolstered by the military. The main resources here are extremely rich soil and good harbors in a strategic location. That's about it.
Oh, and damn good music, food and weather.