What you say about the atheist's burden of proof being larger when the atheist tries to convince a theist as opposed to another atheist is exactly my point in my recent articles on the burden of proof. See, for example, the section on the religion of "Trillionairity" in the article linked below.
What I'm saying is that the burden of proof is like the Overton Window. What sets that window of acceptable discourse? It's history, culture, experience, and so on. So modernity is our cultural background, and that sets the default beliefs which in turn establish the burden of proof in those secular societies.
You're mixing up consistency with epistemic justification. Sure, theism can be made consistent with science, but that doesn't mean theism has been justified. Theism could instead be a vacuous and unnecessary addition that's easily eliminated by Occam's razor. Burden of proof applies to whether some belief is rationally justified, not just to whether it's logically consistent with some other beliefs that have been independently justified.
