Edit: I should say though, right on for pointing out the material issue. You got the meat of it right in that it's overall spending that matters, not just income tax. You "showed your work" correctly, you just plugged in the wrong numbers. That means you get an 8/10 from me.
Edit2: I read the parent's post too quickly in my haste to make a point. However, neither of us considered the contribution of local taxes, as discussed below. I believe that that definitively answers the question of which state spends more per capita.