To even do a "test" you are assuming the truth of the axioms already. There is really no escape from epistemology. Axioms are simply accepted on faith, and everything is built on top of them.
> You are assuming the very logic applied at the time of measurement was, is, and remains true.
No, I'm not assuming that.
> Epistemology relates to how we know what we know.
That's why I added "I remember".
If I can't trust my memory at all, then it doesn't really matter what I do.
But I can put that as a disclaimer over everything if I really want to. I don't have to assume.
And I feel like you've gone way beyond the original scope at this point. If I don't feel like considering the "brain in a jar also the brain only started existing 2 seconds ago" theory right now, my decision to ignore it comes long before I even start worrying about science. If my decision is wrong, it's not a problem with science.