The three conceptual divisions are: basic information which is to be explained (things taken to be true: i.e., believing in God's existence), the explanation which will be found acceptable after the problem is solved (the argument which you are to provide), and the other things implied by the explanation (things implied by the argument whatever they happen to be).
I'm not debating this issue at this time. For the sake of simplicity, let's take what you say as a given. This issue is not relevant to the point that I am trying to make.
You also show a concern with establishing my assumptions when I have clearly stated that my intention is to make no assumptions; (...) Believe me, your example, "if one of the requirements to set up your math was to accept that there is spiritual and evil data in the world, notice how troubling that would be for your paper", is not troubling to my paper at all. If you were to attempt to solve a problem where belief in that requirement were necessary to the solution, all the results of my paper would apply as well to that starting point as any other.
So, if your paper requested that a bystander accept that there is spiritual and evil data, this would not be an assumption? That seems like a big assumption to me.
You comment that my "paper doesn't work if there are no external 'truths' per se". That is a complete falsehood.
So, if there is no such thing as 'knowable data' and no such thing as 'unknowable data' is your paper still valid? Then why call it 'knowlable data' and 'unknowable data'? Why not say there are two fictional categories for data 'ipsi data' and 'upsi data' and tell your reader that these categories have nothing to do with reality, they are just abstract categories which you can sort things? Does your model work if there is no criteria by which to put some data in the 'ipsi data' category and no criteria to put the remaining data in the 'upsi data' category?