Not sure what causes the water to turn white. Did the plants decay in your pond, what is the volume and depth of the pond, the water temperature?
I have a tub outdoors, probably 50 litres / 13 gallons, with water lilies and lots of other semi aquatic plants in it. I have mud as substrate as that’s the water lilies’ natural substrate. The tub receives direct sunlight about 3 hours a day, so the temperature fluctuates a lot during the day (and night). For that reason, I don’t have fish in it.
I never have any algae or bacterial bloom since day one, so I’m wondering if the quantity of plants, water depth or temperature could be the cause of your problem.
My floaters also have long roots as you mentioned, and I suspect that it has something to do with the lack of nutrients in the water. I never remove any dead and decayed plant material during the growing season but drain the water in winter when the lilies go dormant. The water pH always remains at 6.8, ammonia & nitrite = 0, nitrates always under 5 ppm.