I think Gelsemium sempervirens would be hardy with you and does make a totally thick and evergreen cover. There are single flowered, pale flowered and double flowered forms, that bloom, briefly in Spring. Another nice vine is the crossvine, and that may be evergreen for you, also.
I think they could both bring down a flimsy fence or trellis.

I can really see some background bamboo or horsetail(6-10') growing all along what looks like a reed fence, and then some shorter ornamental grasses at 4-5' to fill out the front.
It would match the style of the fence and grow quite a bit taller than your fence to screen out the neighbor windows which are so close.