Well, isn't that just saying "ok, we can assume that contradictions can exist, but it wouldn't be very useful." I.e. if contradictions are possible, then it's difficult (impossible?) to come to any logical conclusions. But like I said, that just means that it's not useful, not that it's not true. Maybe it is true, but only about God? We could still use logic IRL, but in discussions about God, we have to accept that he can do logically contradictory things. Can't we do that axiomatically?
That's a genuine question btw. I can't think of a reason why we can't. If we only use the current rules and axioms of logic because they are useful and approximate reality rather well, can't religious people just say, "well, that may work for approximating everything else, but it isn't very useful for talking about God. We need to assume that God can create a rock that he can't lift, and then simultaneously lift it, otherwise there's no way that we could possibly understand Him." It may mean that you can't use logic to determine whether you can trust God, but as you know, religious people don't use logic to determine whether they can trust Him in any case. It may also mean that anyone can claim anything about God, but as you know, that may well be the point
It's far too weird a road for me to go down, personally, and it's a lot easier to just say that God can only do things that are logically possible, but if I had the ear of an omniscient being, I might as well ask the question.