How skepticism and atheism fails to speak to 3 kinds of rational argument
I would draw your attention to three issues with regards to rationality and reasoning and critical thinking which aren’t brought to bare directly in the question:
1) Experiential proof. I noticed you left experientially off. Experiential proof is in some ways better than logical argument.
2) Abductive reasoning about the future. The challenge of creating proof about the Future–is one which theists and atheists alike are challenged by.. Plus, in the case of many issues, the issue of abductive reasoning about the future–is critical to making decisions. These involve inferences. Being a Christian or test driving Christianity falls in this category for someone who is not a Christian. Logical reasoning as an atheist and rational thinker has to involve abductive reasoning–or the person will result in paralysis.
3) Historical is another form of reasoning which is entirely left off. Logical reasoning as I see witnessed by skeptics is primarily non-comparative and present focused (or that model is at least).
Abductive reasoning and the atheist Google search (link)