There are lots of clematis' vines, both native and exotic, that will produce both flowers and nectar at different times of the year. if your fence is good and strong you might also want to look into hardy kiwi, as it is thick and produces fruit if you get a male and female, but the vines are pretty strong and need good support.
Brushwood, a member here, has a nursery in Georgia that specialized in vines. google gardenvines dot com. He is a wealth of information and very knowledgable about growing conditions etc. And also very friendly and responds to emails from the site really quickly. You might try giving him a pm or ask on his site.
ps. there's also a really cool plant finder page on his website where you can put in criteria like zone and deciduous or evergreen, flower color etc. and it gives you a list of plants! So fun!
Best of luck!