You might be able to straighten these boards out with heat (no moisture necessary or desired). Clamp one end, then apply heat on the convex side. A heat gun works well, but you need to be careful about scorching the wood. It will take a while for the heat to penetrate a 2×2, but you don't need to impart a lot of bend. Try to apply the heat over most of the bend, but concentrate it where the bend is worst. When it's good and hot, pull the end toward you. Over bend, as there will be some spring back. Remove the heat, and hold it in position for a few minutes. With that large cross section, it will take a while to cool. I straightened out an oak crown molding that way one time that looked like a ski. Worked like a charm.
But having said all that, I'm wondering if cedar is the most suitable wood for your project. Have you considered others?
But having said all that, I'm wondering if cedar is the most suitable wood for your project. Have you considered others?