To address the (a) versus (b) issue, a more appropriate viewpoint is "children do well if they can". A fabulous resource for working from that point of view and identifying lagging skills is The Explosive Child book and corresponding website livesinthebalance.org

I have also found the Boys Town parenting hotline gives advice that is not carrot/stick or reward system.

I would also suggest the book "Why Bright Kids Get Poor Grades" because your child may have risk factors for underachieving. (And underachieving is a cause for mood problems and poor outcomes )