Actually in Baton Rouge you are in cold hardiness zone 8 and heat zone 9. Some choices for such a vine that are evergreen and blooming include:
Chinese Wisteria (Millettia taiwanensis)
Tangerine Beauty (Bignonia capreolata) - semi evergreen
Evergreen Wisteria (Millettia reticulata)
None are invasive but the Crossvine can really run long distances if there is something against the arbor for it to climb onto.
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