The good news is all the large common carp (not sure if little ones remain) have been fished out. With the carp gone, the water clarity improved greatly as I can now easily see ~4' deep rather than ~1.5' from all the carp-generated suspended solids. The bad news is the aquatic weed growth is on steroids. Early in the spring there was a good phytoplankton bloom light green in color. As the water temperatures increased, the light green color began to decrease as the weed growth began to increase. The water became increasingly clear with the exception of when algae attached to the bottom of the pond began rising and introduced some turbidity. Surface algae remains on the perimeter of the pond in most area and does not look like cyano-bacteria. The water is now once again very clear.
3Ponds, the problem you now face is the direct result of removing so many carp. To be sure, carp can be a problem that causes harm when their standing weight is excessive. But carp do something few other fish can do. They aerate the benthic sediments and mobilize nutrients increasing the production of phytoplankton and increasing the carrying capacity of fish that directly or indirectly depend on the food chain that arises from the phytoplankton. A good phytoplankton bloom and even a reasonable amount of turbidity will greatly reduce the plant problem you are mentioning. IOWs a sufficient standing weight of carp will probably put you in better place than you are now while not getting you into the situation you were before.
I'll probably take some heat for this but this is what I would do were it my water. I would hope that a few carp remain. I would take the pressure off of them and allow what is there to grow until there begins to be a turbidity problem again and then I would harvest the carp more sparingly on an annual basis. I've read somewhere that around 180 lbs/acre (200 kg/ha) of common carp begin to be problematic but that this can vary being a higher number when the water is more fertile. Did you weigh what you removed or can you provide an estimate of the total weight of carp removed? Not knowing anything and assuming a problem at 180 lbs/acre .... a harvest of 50 lbs each time turbidity becomes a problem might give you the best of both worlds. If they spawn well. The YOY are incredibly good food for predators. Just consider them a prey fish that you have to manage. Just like TP are prey fish you have to manage. Except with TP you will have to buy them and put them in every year. With Carp you might have to remove a few every year or two. Given you would need to remove carp, I would only fish for them when you intend to remove them. Don't make them more difficult to catch.
I found the article to which I referred to above.
Read this if you are interested.