I think if you call the property manager and explain the situation, most of them will understand and be reasonable. If not, you don't want to be a tenant for that company anyway.
Tell them you can provide a letter from your new employer verifying that you will start working and your new salary amount. Also, you can show them your paystubs from your similar job on the mainland. They will run an credit report and call your previous Landlord too.
Good luck & Aloha!