The tough part of getting rivercane is that from settlement times, land growing cane was seen as prime farmland. Thus very few real extensive canebrakes are left in areas long settled. Cane was good fodder, and easily cleared by burning. Look at John Filson's early map of Kentucky. He labelled large areas with "abundance of cane" as part of his promotion of land speculation. To further confuse things the lowlands of VA are warm enough that several Asian species have made themselves at home in Tidewater and NoVa.
All of it makes good arrows if you find it close to the needed diameter and spine. No one is gonna come up to you and complain your arrows aren't "primitive Indian" enough 'cause they're the wrong species of 'boo!!