I agree with you that because these type of phrases are tossed around in our language to this day, there is no evidence that Daniel was not using common nonsense phrases then. We say 'our whole heart' and 'the ends of time' merely to describe a size, and I don't know if Daniel had any idea of the actual shape of the earth just from this.
But, you say he did not repeat 'ends of the earth'.
I do not see the point. If he later said 'whole earth' wouldn't this include the same ends? The tree would be visible to everyone anyway if the earth was flat and the tree covered it. So why would he need to repeat the 'ends' part again anyway?