Alas, my fears were unfounded, and this plant spread into several dozen four-foot stalks loaded with yellow blossoms. The first flowers appeared around the 20th of July, and seven weeks later the plants are showing no signs of letting up with the color extravaganza.
I have no magic formula for the success with these flowers beyond the fact that I simply transplanted them in an area that was partly shaded, just like I found them, though one might suspect that I used the horticultural equivalent of a product like HGH. The spot the plants occupy has traditionally been a poor place for plants to grow, as road salt from the winter tends to run off my driveway and the street into this spot. The woodland sunflowers, though, seem to be thriving in the slightly salinated soil.