Maybe it is missing your pet theory, but the article has a definite point and Priest argues it at length. You seem not to have grasped the article because you refer to logic as something singular that should not be deemed superior to other modes of thought, while the article demonstrates there are many different, mathematically rigorous conceptions of logic.
Epicycles are a non-sequitur here, because there is not a particular proposition that you set out to prove with whatever explanation you can find. Rather the goal is to find a logic that does not break down when presented with paradoxes.
There can be an infinite number of different rigorous conceptions of logic, while at the same time there are also an infinite number of modes of thought outside of logic .. we know the ones like instinct, superstition, and religion that are considered inferior to logic. Is it possible for there to exist a mode of thought yet to be found or invented that is better?
I wouldn't say we "know the ones like instinct, superstition, and religion [...] are considered inferior to logic". They are not comparable, unless you formulate criteria for what is better, and then you can easily bias the comparison towards one or the other.
If there exist an infinite number of modes of thought as you posit, then yes it is possible that the best one is not among the ones we know of now.
I don't really think of it this way though, because logic is not supposed to give us something new, not supposed to give surprising conclusions. Logic formalizes the steps you can take to arrive at valid conclusions. However, what constitutes valid conclusions is ultimately based on our intuitions, it is what the logic is founded on (comparable to how mathematics is ultimately based on accepting axioms).
