In my opinion the blanket weed will grow just as well in still water, its main requirments are light and nutrients, in that order.
You can buy various products and chemicals that can control this fillementus algae or small bales of barly straw or lavender.
If its possible to exclude the light for a spell until its all died off, I think this would be good option, if you can sheet it or board it over (although not too pretty)
What cured my small pond of this weed back in the spring was the introduction of tadpoles, which ate it, I them allowed a small water lily to cover about 3/4 of the surfice and also controlled some duckweed to help filtre out the light. Hope this helps T bird+
Ps You may like to think about some shading with some shrubery as a long term plan. Good Luck.