Aloha Jacob, I'm a retired submariner who's lived on Oahu for over 30 years. I post to the MMM forums as "Nords."
If you want to invest in real estate, then invest where the numbers make sense. "Buy a home at every duty station" was about as good as we could do in the 1980s before the World Wide Web, but you have the tools and the team-building skills to invest anywhere on the Mainland.
In general, Oahu real estate is fully priced and doesn't meet the 1% thumbrule for investment properties. Your housing allowance seems like a lot of money until you start shopping.
On a military housing allowance, the easiest and least-risky way to invest in Hawaii real estate is to house-hack with roommates. If you want to invest in more rental properties with your excess BAH then I’d suggest looking anywhere else on the Mainland where the 1% thumbrule works (at least a 6% capitalization rate)-- and where your invested dollars will go a lot further.
On the other side of buying a home in Hawaii while you’re on active duty, I get many unhappy e-mails and other comments from people who’ve bought here and then can’t cover the sales expenses. Your property is highly unlikely to appreciate enough during 2-3 years to pay the 5%-6% realtor's fee (paid by the seller) in addition to the closing costs (both buying & selling) and any staging fees.
When military families inevitably transfer off the island, they’re not able to cover all of the landlording expenses either.
House-hack on Oahu and buy your investment rental properties elsewhere.
Side note: if it's any consolation, the VA has lifted their lending limit on loans originating after 2019. From now on the only limit on your borrowing is whatever the lender will give you for a debt-to-income ratio, and the VA guidelines for lenders will sometimes encourage them to approach 50%. It depends on the lender now.