Instead of each strip having to rotate rigidly when you open/shut the blinds, allow each strip to freely rotate but with a(*very* weak) spring. So that way if the rotation is not obstructed by anything it will still rotate correctly; otherwise you can still open the blinds and the offending strips will simply not rotate. For example if one is behind the other on the wrong side and thus prevents both of them from rotating. That way you can just open it, and then go around and fix the ones that won't open, instead of being frustrated because of not being able to open it, being worried about not breaking it, and having to figure out which ones are blocking it from being opened.

also, venetian blinds should come with extra strips since if one is damaged you can't really get a replacement.