I've had pretty good luck so far doing an alternating system of bleach and Star right purifier.
Since we travel.quite frequently and use the watermaker fairly regularly the water in the tank stays pretty clean and we'll agitatted.
I've chosen a plain household bleach and add about 16-20 ounces (500ml) when the tank is 3/4 filled then fill the rest of the way.
This solution is not strong enough to harm things but will prevent growth.
I do not back-flush the watermaker with this tank .. even if it means using the watermaker without a flush for a few days.
We try to use this tank quickly; laundry really helps :) .. when the tank is low, a freshwater refill is made and we can again flush the watermaker (as a side note, the Dow membranes have a stated ppm rejection/tolerance number started in the literature .. and while I don't remember it offhand, I do remember it being more than I expected.).
The next refill will have two teaspoons of the Starbright water purifier (diluted with 20 oz of warm water) added to the tank when about 3/4 full.
Then, we are set for a month or two of regular use and dock-water fills.
I will (perhaps brazenly) say that all growth need not be fretted about. If the water is regularly treated then the growth will gradually go away.
I do use a test kit available for hot tubs/pools to test ph and chlorine after treatments as well as a TDS meter ($16 on Amazon) to make sure nothing is getting out ofnhand. (some ockdwater has been extremely "hard" and tests badly so we try to avoid it .. calcium in the shower head and all that...)
So far, so good :).
SM 209 Adagio
Maryland, USA .. waiting on new sails :)