That trough is way too small to allow a decent root ball for a vigorous climbing plant. It’s also very high maintenance, would need daily watering. Clematis is definitely out as pots don’t give them the cool roots they need. Is there any garden within reach of the patio? Then you can use hops, Russian vine, grape vine etc. trained to reach your pergola. But it will take 3-4 years to become established, plus the annual clearing up/pruning etc. My wife’s suggestion was the same as your first thought, a sail, and use the pot for something smaller and annual. Or get your pergola, use scrim netting over it for shade, and grow annual (cup and saucer plant for instance) up the supports.