This isn't really a solution that would fall under the permaculture banner, in my opinion. The website doesn't even address underwater use for their product, which they are clearly trying to sell to anyone trying to work at-grade with concrete.
I would look to other methods, including recirculation of water, possibly through a physical filter, such as a sand filter. Such can be made using a food-grade 55 gallon drum, several grades of sand, from coarse to sharp, potentially even diatomaceous earth and charcoal. I would put the charcoal at the bottom, the diatomaceous earth on top of that, and then the sand, from sharpest to coarsest, in discrete layers. I would probably put some kind of water-permeable membrane, like a cloth of some kind, between each layer, and lining the barrel.
Lastly, I would put a large scoop of silt from a healthy waterway, right in where the reeds and rushes are growing, atop the top layer of sand, and I would perhaps plant some reed species from there into the top of the barrel. Hell, I'd look to see if I could scoop some local filter feeders for the top of the barrel, if there were some kind of clam living there, just to help filter stuff out of the water and process it.
You could make as many of these as necessary, and power them with cheap solar pumps, or really simple wind pumps.
Lastly, I would, if possible, find a local species of minnow or aquatic snail that eats algae. If you filter the water constantly, there will never be enough algae to cause a population explosion, and those that do live there will quite happily keep your algae down.
The other thing you could do has to do with the colour of your tiles. If they are white, they will reflect and diffuse light better, and the UV radiation from the sun will kill any microbes in the water or on the surface.
The anti-fungal, anti-microbial agents will simply be poisons. You can simply chlorinate the pool easily enough, or bleach it far enough in advance of ritual bathing, and then again, after. These, however, aren't really permaculturally-aligned solutions.
But good luck, and let us know how it goes.
A human being should be able to change a diaper, plan an invasion, butcher a hog, conn a ship, design a building, write a sonnet, balance accounts, build a wall, set a bone, comfort the dying, take orders, give orders, cooperate, act alone, solve equations, analyze a new problem, pitch manure, program a computer, cook a tasty meal, fight efficiently, die gallantly. Specialization is for insects.
-Robert A. Heinlein
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