Any algae is caused by excess nutrients in the water column. Reduce and eliminate nitrate and phosphate and there will be no fuel source for the algae to grow. Look into meowsers stinky thread - she vaccuumed a part of her sand bed and got a bunch of excess nutrients out, and eventually her water quality will improve.
I say the best thing you can do right now is add an emergency algae scrubber made out of a 5g bucket suspended from above the tank. A properly built scrubber takes about a month to rid your tank of algaes, but it's well worth it, and will reduce and eliminate all excess nitrate and phosphate from the system. It will compete with your dinoflagellates and get rid of them. It's definitely worth a shot.
About the whole no water change thing:
I only do a water change once a year if I need it. It's not for everyone, but it's worth it to me. It all just depends on your filtration, salinity etc.
I use kalkwasser to make up for calcium and alkalinity when necessary. If calcium is out of balance, I use calcium chloride. If alkalinity is out of balance I use baking soda. If I need to add magnesium, I set a cup of epsom salt in my sump and let it dissolve. For trace elements, I dose a capfull or two of Kent's Essentials every now and then, but mainly for the iron supplement, which lets my algae scrubber grow really green.
