I grow organic Woad (Isatis tinctoria) and organic Japanese Indigo plants (Polygonum tinctoria) both of these are versions of cold climate indigo that grow well in Minnesota. Neither are native to North America, but both grow well in the upper midwest.
Woad is notorious for spreading quickly. So quickly that it is considered invasive and noxious in many western states in the United States. To learn more this is a detailed report of the plant, and you can find your state.
While dyeing with fresh Indigo leaves is lovely, extracting and saving the pigment so that it is shelf stable is incredibly exciting to me. Below is the process I used this summer to process Japanese Indigo leaves into shelf stable pigment using the fermentation method.
Remove the plants now, and compost. Then you can move on to alkalize the liquid. Remove ALL plant mater from the bucket. This could take a while. Then, add about 1Tbsp slaked lime per gallon of water to this bucket. Stir to dissolve, then stir this liquid back into your large container.
Use caution when adding slaked lime to water, as the solution will be highly alkaline. Avoid splashing the liquid, and if it gets on your hands or skin rinse immediately with fresh water.