This is Cardolan, and no longer Arthedain. And what Tolkien is very likely trying to do is to recall the remnant of the Isle of Almaren and grant to his creation, Frodo, the supreme grandure of a grant of commensurate glory of letting the Ringbearer walk this most anciently worked piece of Arda. Think of it as an 'early payment' for Frodo's sacrifice. Here we see two Ringbearers (Frodo and Sam), Merry (who is to become killer of the King of the Nazgul), and Pippin who faced Sauron or The Voice of Sauron or the King of the Nazgul in the Palantir ( the Palantirs were probably wrought by the Noldor and perhaps by the House of Feanor itself.
This grant was probably contrived through Gilfor Inglorion (of the House of Finod of Nargothrond). Farmer Maggot's mushrooms probably couldn't have secured this level of 'key to enchantment' if they dosed with anything and it was likely some food fed the three 'starters' during that meeting which led yo their trip to Cardolan.
Tom Bombadil has something to do with Tulkas. And The Lamps probably met when they fell right in Cardolan but destroying flame was diverted in the nick leaving that souvenir of original Arda as unspoilt and so perhaps Tom Bombadil can't leave it.
Almaren had been an isle on a lake and the light from the two Lamps met and blended there. There should be then a lot of Almaren symbolism in the hallway three chapters, The Old Forest, The House of Tom Bombadil, and Fog on the Barrow Downs.