I tried rolling it up at the headstock like you have it, Paul, but that's not working either. It's really not a big strap, but the padded portion is kind of thick and resistent to rolling. I think ultimately, once the strap gets broken in and softens up, it will roll up more easily.
Until then, I guess I am going to try to attach it to the outside of the case, but I doubt I'll go so far as to install an end pin and heel button. Maybe I can come up with a small pair of saddle bags that I can slip over the case handle.