There are many holes in your argument. First:
''Any number of ideal rational thinkers faced with the same situation and undergoing similar throes of reasoning agony will necessarily come up with the identical answer eventually'' How is this known?
It is known via logical deduction. If ideal rational thinkers are faced with a symmetrical situation and reasoning alone is the ultimate justification they will reach identical conclusions.
This must be true if reasoning is objective as arithmetic is.
Let's say for a moment that it's true, what does it matter for us? Humans cannot be ideal rational thinkers and even if somehow someone could, how would we ever know?
I agree we cannot be ideal rational thinkers. Our biological limitations alone guarantee that. But that does not mean we should not try. Indeed it would be idiotic not to try.
C.S. Lewis wrote a nice discussion on this point.
https://m.youtube.com/watch?v=MtTeCyrgjIQ&t=160s
Your arguments fail to really prove anything as they offer 0 evidence of anything that it's claimed there.
Not sure I am following you here. My arguments are simple logic that anyone is capable of following. What evidence are you looking for?
What a subtle way to tell him he's not human. 
Ha ha I doubt the subtlety was intentional but that was funny.
Well, if you agree humans cannot be ideal rational thinkers, then whats the point of bringing it up? We gain nothing with it.