Are you familiar with Sextus Empiricus? If you like intransigent skepticism, you'll love him. And the SEP just published a new entry on him! While you are at it, you might want to look at this entry on a priori justification.
You are trying to answer Descartes' Evil Daemon argument. That is futile, because the whole point of the argument is to be unbeatable. But suppose you did come up with an argument against it; I can always come up with an even stronger "daemon" or whatnot that can defeat the argument. (There's always the classic "How do you know you're not dreaming right now?" also from Descartes.)
Perhaps you are not actually searching for something to defeat radical skepticism, but instead are trying to show everyone else the true nakedness of their epistemic pretensions?
If we can have no a priori knowledge, it means skepticism wins because everything is based on faith. Given this, I try to find a means to make a priori knowledge work despite objections, both of this sort and skeptical.
If this is right, then radical skepticism wins entirely. The point is if it can be shown false on probabilities.
Yes and no. I do believe it hopeless, but I search because I'm looking anyway,
I've raised arguments for philosophical scepticism before, which have mostly been argued against in a Popper-esque manner of arguing that even if we don't know anything with certainty, we can have legitimate knowledge on probabilities.
The problem with this, however, is how you answer a sceptic about the notion of probability having a correlation with reality. Probability depends upon axioms of probability- how are said axioms to be justified? It can't be by definition, or it has no correlation to reality.