Someone needs a course in binary logic and proof theory.
It all sounds so wonderful. I do not believe that god does not exist. I just don't believe that god exists. I am all rational, but also do not have any burdens of proof. Act of faith vs rationality, and all that. Amazing, right?
Wrong. Let this be cleared once and for all. All scientific/logical theories are by definition only explanations/observations of the truth and not the truth themselves (the map is not the territory and all that jazz). Thus, the statement that "Gravity exists" is logically the same as "I believe that gravity exists". The reasons for your beliefs and your ability to justify them will qualify the strength of this belief. Hence, a rational person will have no qualms stating that "gravity exists" but will need to qualify his belief in god by saying that "I believe that god exists". "Belief" is a qualifier to the strength and justification of your theory - it doesn't change your assertion of the truth value of your theory. Knowledge is only a representation of the truth, not the truth itself.
Hence, I believe that god does not exist and I do not believe that god exists are logically one and the same. Any attempts to try to prove otherwise miss the important distinction between the truth and the representation. What is wrong with these modern day atheists? Don't they even have the balls to say "God is dead, and has always been" (or something like that)? Come on people, you have Richard Dawkins as your intellectual fountainhead. Show some bloody guts.
There are exactly three major logical positions to take w.r.t the existence of god. "I believe that god exists", "I don't know and the world will in all probability never know", and "I believe that god doesn't exist". (Actually there are four - one can always say "I don't bloody care".) There can be variants within these major positions, but to try and get out of committing yourself to one of them broadly is just intellectual dishonesty.
If all you want to talk about is the burden of proof, here's how you frame it - proofs are either constructive or by contradiction, but can never be by assumption. A positive assertion ("God exists") will typically need to have a constructive proof or a strong reductio ad absurdum. As long as you can thrash the positive proof, it will be considered a good enough negative proof. An example of this is the god of the gaps rebuttal given by atheists.
When it comes to God, or the final explanation, the absence of evidence is pretty much the evidence of absence, irrespective of what Carl Sagan says in the preface to A Brief History of Time. All we need to remember is that the evidence need not necessarily be a positive empirical observation. Counterfactual reasoning is often the only way of determining causuality.