Here's an idea, if you have a 4 door car, drive for Uber and Lyft on the side when you are off from your duties. There is decent demand on Oahu and you can take whatever you make that you don't use for gas and maintenance to pay for flying.
Other than that, there isn't really a way to get this funded easily. The Ed Center won't pay for anything other than just straight up college these days due to the budget cuts.
As far as what your GI Bill will cover, it will cover Part 141 training towards Instrument/Commercial and higher. Chapter 30 (if you had the $1200 taken out your first year) will cover 60% of costs for 36 months, and the Post 9/11 (Chapter 33) will cover 100% but only up to roughly $11k per year for 3 years.
I did a lot of my flight training at HNL south ramp and Kalaeloa Airport, which ended up being self-funded due to the lack of value the HI flight schools offer. IMO, if you're dead set on using the GI Bill to fly, you're better off just getting your PPL here and flying for fun to other islands, waiting until you PCS to the mainland where you can get a variety of schools that offer better return of your GI Bill investment.
Honestly, the best way to use your GI Bill in aviation is to attend a college that actually will include the training in your degree plan, so you get a college degree, CPL/CFI/CFI-I, and the 1,000 hr RATP exemption all in one. The sole program in the state that existed through HNL Community College closed their doors recently, so you're out of luck there.