Where did Radagast dwell?

[Legate of Amon Lanc]

This topic is supposed to be devoted only to finding out where and eventually when did Radagast dwell during his stay in Middle-Earth. But before I unfold before you more complicated scheme, we need to clear something up. With this question we start, and I am hoping to get it answered, for it is the main question I have concerning this topic.

I am posing you a serious, plain, wholy understandable question and I am expecting a serious and wholy understandable answer.

WHERE IS RHOSGOBEL?

One would say, quite a basic thing. It's almost as if I asked "where is Minas Tirith" or "where is Orthanc". Everyone knows where Annúminas is, everyone knows where Durthang is, even though they are not almost mentioned in the story, certainly not more than Rhosgobel. But where is Rhosgobel?

On the map in LotR, at least on the one I have, it's not marked at all. Of course, why not, I won't expect it there as Rhosgobel does not play any significant role in the story (though the same could be said about many other places that are marked).

In the Hobbit, it's not on the map as well; and as in the former case, I won't even expect it there. Maybe under certain circumstances we could take one of the woodmen villages mentioned there as Rhosgobel (cf. below).

But in the chapter "Queer Lodgings", we read:

Originally Posted by Gandalf, to Beorn

perhaps you have heard of my good cousin Radagast who lives near the Southern borders of Mirkwood?

Southern borders. So I would expect something, well, quite close to Dol Guldur, something like that.

That's the last time we hear about Radagast for a long time. Next time, Gandalf meets him in FotR and tells to the Council of Elrond something about him:

It was Radagast the Brown, who at one time dwelt at Rhosgobel, near the borders of Mirkwood.

Now it's just "borders of Mirkwood", not "southern borders", but that still corresponds with the previous.

Later, when the Fellowship is preparing to depart, Elves and Rangers and sons of Elrond are sent out to check the paths and surroundings.

...and some of these had crossed the Mountains and entered Mirkwood, while others had climbed the pass at the source of the Gladden River, and had come down into Wilderland and over the Gladden Fields and so at length had reached the old home of Radagast at Rhosgobel. Radagast was not there; and they had returned over the high pass that was called the Dimrill Stair.

Now this is the part that is opened to most speculations. "Over the Gladden Fields" seems to imply that Rhosgobel was lying on the other side of the river, in the same latitude. This would also correspond with the words "near southern borders of Mirkwood". Also, if the scout returned over the Dimrill Stair, then they probably went south meanwhile.

The impression from what was quoted before is that Rhosgobel could be in the latitude where the Narrows of the Forest were. Karen Wynn Fonstad in her Atlas of Middle-Earth (generally a very credible source) places Rhosgobel at the global map of the 3rd-Age Middle-Earth somewhat north of Dol Guldur, in the same latitude as Mirkwood's East Bight.

But then we have the Unfinished Tales. There, Rhosgobel is mentioned only once, in the notes to "Istari" (#4):

In a very late note on the names of the Istari Radagast is said to be a name deriving from the Men of the Vales of Anduin, "not now clearly interpretable." Rhosgobel, called "the old home of Radagast" in The Fellowship of the Ring II 3, is said to have been "in the forest between the Carrock and the Old Forest Road."

*ahem* Now, as you can see, this quite opposes what we have just said. "Between the Carrock and the Old Forest Road" is somewhere near Beorn's house - and that's neither "near southern borders", nor much close to the Gladden Fields or the Dimrill Gate. I can't find Christopher's map that was in the UT now, but I believe Rhosgobel is not marked there (or am I mistaken?). However, the funny thing is that Karen Wynn Fonstad, in the very same Atlas I mentioned above, marks Rhosgobel on two maps (regional map of Wilderness and regional map of Misty Mountains) according to this statement, quite in opposite to where she put it on the global map of the Third Age. Looks like she did not even realize this difference (which seems indeed strange?).

Now, where is Rhosgobel, then? Is there any other evidence I did not mention, that solves this problem? Some Letters, for example? And what shoud we take as "canon"? Personally I would skip the "late note" and listen to what is said in the books. However, the UT text is the only one where the placement of Rhosgobel is stated more concretely, and since it's a "late note", Tolkien could have had his "last version" prepared - but what of the mentions in the Hobbit and FotR?