re: how would you?

The curves appear to be almost exclusively decorative and providing minimal support to the structure. Having said that, I would edge join enough boards to create a pannel with a width slightly larger than the curve and cut it out on the bandsaw. Ti get four identical pieces, you have a couple of options. 1. Stack your four panels with double sided tape and cut all four of them at once on the band saw. Or option 2. Cut a pattern from hardboard or similar material. Stick it to a panel with double sides tape, cut it out on the bandsaw, then use your router table with a pattern bit to trim the piece to the pattern exactly. I would prefer option 2 because I am comfortable witht this method. The trick is to take the time to make a good smooth pattern. Its worth it since you will likely have it forever.