Inzilbêth of the Dúnedain

Well, since Trotter tells the Tale of Tinúvel already in the first draft, and Tolkien still mentions the idea of communicating with animals, in a slightly modified way, in the second draft of the chapter, when he says of Trotter that he could understand some of the language of animals, I'd say he was rejecting the idea of direct communication. I could see Tolkien hinting at the idea of the Arnorian rangers, due to the close communion they kept with animals in the wild, coming, as he says of Trotter in the second draft, to have some understanding of their language(much in the same way and for the same reasons that the elves understood the language of living things and even of stones in his universe). In his indirect mention of it in that quote from ch. 9, Tolkien most certainly manages to hint at this possibility, without fully commiting himself, given that he attributes it to characters in the book. I'm pretty sure though, that he most certainly dropped, maybe because as you said he thought it a little too radical, the idea of direct communication between Aragorn, or the Nortern Rangers and wild animals.