I think we need to see som pictures or drawings. 12" radius on the back?
These are the plans that Mike sent me. I did make some minor changes but there close.
I did change some measurements to fit my needs. The height changed to 57" so I changed the rear radius to match @ 57" instead of 60". One wouln assume that if you are going 48" high then the large rear radius would match @ 48".I also went with a 20" radius on the front and back instead of 19". You will need to find the piviot point for the large radius and the height of the small rear one. Just start draw some radii on your side plywood and keep moving untill things look right.
Now back to your question. It has been my experience that some sheets of plywood are more flexable than other and also length wise or width wise is different. I used Moisture resistant 5.2mm Luan and half of my sheets were like rubber the other half were as stiff as a board. I would do as I did this time and buy your sheets to make sure that you can flex them enough.
I did hose one sheet down (of the stiff sheets)(The stiff sheets were birch and looked nice) to get to bend into the front radius for the inside. Remember I did use "Moisture Resistant Luan" and I live in dry Denver and it was the middle of summer. I hosed it down (both sides) for about an hour, it was more flexable but it still took most of my strength to push it into the radius! It dryed out and I have had no problems.
I hope this helps. Have fun. The end product will be worth it.