I wait until the plant dies then I pick it. Not sure how it does if you pick it and then dry it? The skin and fibers should be to the point where they want to fall off on their own.
I make lots of cordage with dogbane, here's my method:
Split the shoot equally in half with a knife. Don't pound with a stone to remove woody material - you will break the fibers. After you split it break off the woody material in 1'' increments and separate the fibers and skin - this should come off easily. Once both halves are done, match the thinner end with the other thicker end so you end up with a length of fibers with equal thickness. At this point twist back and forth with hands a few times to remove the skin. You don't have to get all the skin off, its fine to leave some on. Just try and get the majority. Then give the processed dogbane a few twists in one direction and its ready for twisting into cordage - look up Flemish twist method if you need at this point. Sorry if I'm telling you something you already know, I just like to talk/make cordage!
