Curly-leaf can spread fast as you are seeing. It spreads by seeds as Dr Dave says and also by winter buds called turions that form on the stems. The seasonal die back noted by John and Dr Dave is due to the plant being a cool water plant that flowers, produces seeds, and turions early season, then most plants die back during the warm water season of maybe late Jun, Jul-Aug-earlySep depending on location and water color.
In NY in late June IMO you are too late to stop the formation of seeds & turions for next seasons crop unless you have kept all plants pruned close to the sediment. You have to cut or prune it close to the bottom early in spring before it reaches the surface to stop formation of seeds and turions. This helps slow the spread.
Since your colonization is supposedly still small you could spot treat the area with Aquathol Super K or Hydrothol 191 - both granular herbicides that work well on smaller spot treatments of curly-leaf. Smallest containers I think are 10 lb pails and a little pricey. Hydrothol in higher concentrations and large applications can be toxic to fish so be careful if you use that one. But if you use it just around your red lily it should be okay. Do not over dose; read the label and instructions. You will see effects in several days on killing the curly-leaf. You probably will not eradicate all the plants with one treatment. You will probably need to re-treat again mid-fall(early Oct) when turions sprout and are 2"-6" tall or treat early next spring well before it reaches the surface. Neither herbicide should kill your water lily.
One good thing about curly-leaf is it provides good short plant cover and habitat during cold water of winter, very early spring when about all other plants are dying and collapsing. Another good thing is it uses lots of nutrients in cold water thus competing against and reducing the amount of cold water algae.
http://www.midwestaquacare.com/product-labels/Aquathol-Super-K-label.pdf http://www.aquaticbiologists.com/Labels/Hydrothol191Gran.pdf
