Even if you use a static raft system or wick system, you still need to have an aerator to oxygenate the solution or you will have problems for sure with anaerobic conditions.
The biggest problem with organic nutrients is the lack of control of the nutrients. With hydroponics you can add just nitrogen or just phosphorus in precise amounts. Organic products vary by source and the speed at which the nutrients become available. You would probably have to mix a solution and discard it on a regular basis once it gets "used up" and becomes unbalanced. You either dump it down the drain or in the yard, but either way it may still be polluting.
A static system will not be able to support large or long term plants that are heavy feeders.
An aquaponic system would be the most organic, but that is not a static system and you would still need to aerate, circulate,adjust the pH and supplement to keep both the fish and plants happy.
This link is a guide to the pros and cons of different types of systems.
https://www.aquaponicssystems.net/aquapo ... ic-systems
this is a link discussing the challenges of using organic fertilizer in a hydroponic system. I can be done.
https://www.gpnmag.com/sites/default/fil ... 0FINAL.pdf
If you want a static system that will only require you to basically add water, consider an earthbox instead. It can support a variety of plants and you can use organic fertilizer. The reservoir does not need to be circulated and you only need to refill it with water. I warn you that the soil does have a lot of anerobes in it which you will find out by the smell when you dump it out.
Happy gardening in Hawaii. Gardens are where people grow.