We had 4 ponds with lilly pads sticking 4'out of the water. they were 1-5 acres. We bought a product from Pond Boss and spread it as best we could. It cleaned house. It's a granule and we used big plastic cups to sling it out in the water. It's a chore and if you don't have shoulder problems now you might after. It doesn't hurt the fish or the moss. Now the hard part $200 a bag. I think we used 4 bags. It was well worth it. We are off that place now but for three years it was still working. Dragging a pond won't work.
looking like grass carp (not one of my favorite fish) and some chemical pellets I found are the most effective for long term.
then there is this.
A friend of mine worked for a pond management company and said they use 2,4-d to control them and it's safe to use on water. You have to be careful if spraying from a boat to not create waves that will wash it off. Last resort they use their amphibious tractor to remove the stuff. They are really cool but expensive.
Edit: I'm not sure the mixture ratio but could ask him if you are interested.