These are the curtains: https://www.potterybarn.com/products/riviera-stripe-blackout-drape/ -- very heavy. What would you suggest?

IMO -go with the longer rod & more panels..

One rod blackout blinds and drapes that are nice to go with the restyt of the space insted of heavy drapes to give blackout. I would like to see the whole space before really advising .You will for sure need many more panels which ever choice you make . IMO drapes need to be at least 2 x and 3 x even better for width.

Here is what is bothering me about the three panel question. When you push your drapes open, the thickness of the panel another words how much room the fabric takes up when it’s folded together is called the stack. A standard stack is usually about 10 to 15 inches. That would look good on the size windows
That you have. The problem comes in the center. You will have a very large 30 inch or so stack in the middle and two little ones on the side. I think you’re really better off with two rods and a little open wall showing between the windows. Mount your rods so that your stack will just cover the sides of the shades a couple of inches.

We voted for no curtains, and some shades instead with a nice long thin mirror or artwork perhaps on the wall too! Good luck!