Sounds like a good combination if you get a good quality top soil. Watch the bags of compost if you are buying them. Sometimes they have added lime. Mushroom compost and some composts will be alkaline. Peat moss is acidic.
I prefer to go with a balanced fertilizer. If you are going more organic realize that nitrogen will be the hardest element to get enough of. An organic fertilizer with 10-10-10 will not have 10% nitrogen available, some of that will be bound and not available as it will release slowly.
Plant growth will be limited by the amount of nitrogen available. So, you may still need to supplement nitrogen in the early growth stages with fish emulsion, AACT, and side dressings of nitrogen.
In a new bed the soil microbes population will not be very high. It will take almost 3 years for the beds to be at maximum efficiency.
Happy gardening in Hawaii. Gardens are where people grow.