The reflex and deflex is piddly and beneath your attention.
I agree. I love starting with a straight, symmetrical stave, but that is not enough to go through the complicated steps of heating or steaming, and will likely resolve itself.
You are doing things right. I often go two layers on linen backs, but that, of course, depends on how thick the cloth is, etc.. I like to lay down a Titebond III sizing coat on the wood, let it get tacky, then almost saturate the cloth and lay it down, pressing it in with my hands or a roller. You are fine to trim or round the edges as you are doing.
The issue with two layers is it takes a lot more glue to hold down cloth to cloth, so the proportional weight rises. Also,if you used any glue with water in it, which is most wood glues and hideglue, give the stave a few days to lose that water before flexing it much. You want the glue good and dry, and you want the wood good and dry.