I think the real issue, at least for me, is not whether Noe really bult an ark, but that nothing is in it which would contradict an ancient date of origin. Whoever wrote the text of the Noe story, regardless of whether you believe it, lived many years before Christ. We know this to be true for many reasons and the text is also consistent with that fact. But, can the same thing be said about the BoM and what is said in this story about the barges and Jared?
Here we are presented with a text which takes for granted an existence of glass windows. God speaks assuming that people knew about them and therefore would have desired them. This means that the people would have already had developed glass window panes at the time of the tower of Babel, which is outrageously false.
Not only that, but these windows would also have been clear, to let in light. There is another reference to such an idea a bit further on:
As far as I can tell, from what I have available to me, such clear glass did not exist until some time after Christ when the Romans developed the necessary technology. It certainly would not have been known and taken for granted by people from the time of the Tower of Babel.
So, as far as I would be concerned, the problem is not whether this story, or that of Noe, is true. The problem is when was it written. We know that the Noe text is ancient, but not the Book of Mormon. We can only trace that back to Joseph Smith. And anachronisms such as these certainly give every indication that the text was written by somebody to whom clear glass window panes were well known, and not someone contemporary with the Tower of Babel, or anything even close to it.