I've seen euonymous trained up a chain link fence - it looked almost like a hedge. Not sure how fast it grows. You could train your Virginia creeper up but it's not evergreen.

You can experiment with cheap seeds like morning glory, moonvine, and runner beans. Might not get much in the way of flowers or beans, but you would get fast leaves for screening.

Several of the variegated ivies are attractive and not as vigorous as the green. Illicium henryi, I. floridana, Bignonia capreolata and Gelsemium sempervirens do well for me and would provide blockage, but you may be at the limit of their hardiness. Viburnum X pragense, V. rhytidiphyllum, Boxwoods and Taxus should do well also. Keep in mind that competing tree roots will require that planting be given a weekly soaking.

You might want to consider a climbing hydrangea. It's not evergreen but should be dense enough eventually even without leaves to give some winter coverage.

The fastest evergreen vine would be some kind of ivy. I have plenty if you want to give it a try. Just keep in mind that anything fast will want to creep into your yard, devour your garage and anything within 100 feet. I think that climbing hydrangeas are slow growers and clematis need some sun to do well. Some native vines can take a lot of shade. I've been trying to grow a screen as well, in 90% shade, dry, and haven't found anything which works well yet. I will not grow the thugs, such as ivy, since I have spent too much time controlling and eradicating them already.

will climbing hydranges grow in the shade quickly?

No, they don't grow quickly - but they are well worth the wait. I'd suggest that you put a quick grower in also, something that you could pull out when the hydrangea has begun to grow.

Here is a link that might be useful: Climbing hydrangea