Wow, Turks and Caicos. Been wanting to dive there for years.
Water definitely looks like tannins. Looks like the water in the Cenotes in Mexico. Tannins (tannnic acid) are acidic because if they are strong enough in the cenotes they will even etch the plating on the hose ends of a scuba diving regulator.
So it would seem that limestone to neutralize the acid would be helpful for the water, but that is just a guess on my part. Of course the tannic acid like you said is produced by the organic matter (leaves from trees in the cenotes) so removing that would also be helpful.
Maybe I need to come down and take a look.
Any good reefs nearby?
