I hear you on the emotions of the buy vs rent decision. Let me know if you want more help crunching numbers-- we have a number of military investors on the islands who network and help for free.
You also want to make sure you're not asking a barber if you need a haircut-- hopefully your realtor is experienced at working with real estate investors instead of homeowners. You'll get the $3400 BAH whether you spend it on housing or not, so a sure way to put it to work is to go cheap on rent (or house hack) and invest the rest in your asset allocation (equity index funds or REI) where it makes sense. You don't have to dump your BAH into real estate in the same ZIP code as your duty station.
I’m a solar nerd, and we’ve had a grid-tied system since 2005. It paid us back by 2011 and we’ve had free power since then. It’s worth buying (solar water heating as well as photovoltaic) when your electric bill becomes $26/month instead of $250/month. However Hawaii’s photovoltaic incentives are not coming back. Those subsidies did their job and the systems are cheap enough for the markets to compete on their own merits.