Clematis does stay woody and therefore once established does still offer some screen, especially if planted with an evergreen honeysuckle like trumpet honeysuckle. You can then get a longer flowering period and it looks really good.
What about Star Bush (Illicium floridanum)? It looks good used as a screen and is evergreen with beautiful flowers.
I'll probably do nothing.... but I think the best bet might be a row of those evergreen cedar type things that get huge.