It seems to me that burden of proof is an object of discussions and not something that belongs to existential claims. So those who have no motivation to enter into the discussion have no bearing on where the burden of proof lies, only those who want to move the needle in one direction or the other.
Yes, I'm aware. But the set-up is complicated by the fact that scientific modeling is generally assumed to have shifted the case so far along that Pascal's wager is essentially nothing more than buying a lottery ticket with astronomical odds of not coming into fruitition.
Analytic statements are true by definition, the issue being that they do not say anything about what is real. But what my project intends to establish is that any epistemic framework is going to begin with something being defined as true because, as far as I can tell, Munchaussen actually collapses into two options. Either dogma or epistemic paralysis through infinite regress. We either take something as a brute fact, or we can keep asking, "But how do I know that?" So we either embrace radical skepticism, or we accept that something about reality is true by definition. Which is reason to take seriously the premises of the ontological argument as some ontological argument must be accepted, either for God or some godless natural order, so Kant's objection can be dismissed as can Gaunilo's. The tricky part is bridging the apologist's gap and moving from a generic panentheistic deity to God of the Bible.
There is a caveat that separates me from Presuppositional position, in that I don't believe that the Sensus Divinus is empirically demonstrable. I share some kinship with presuppositional arguments, but I'm more concerned with the question of justification in the ordinary sense and not for God in particular. I'm interested in spelling out what it means for something to be a claim, what we mean by justification, what epistemic maxims and techniques are appropriate and why they have force, and similar. More of a complete breakdown of the very epistemic enterprise, a sort of meta-epistemics. I'm not sure who to even begin with in such a project, since my background is far more developed in theology and exegesis than in general epistemics.