Algae need nutrients and ...

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Algae need nutrients and light, if you can limit either of these you can limit algal growth.  

Other than the obvious pontoons, floating balls, surface growing plants, etc. if your lake is deep enough, circulation could be used to draw the algae down below the growth depths.  I'm amazed to hear that algae is growing even under 3 foot of ice, can you see it through the ice?

Otherwise you're easiest assessing the rate limiting nutrient & then determining if you can control its concentration.

Or you could consider predation.

Have you tried varying concentrations of ozone and AOP's for the oxidation step?