The Heirlooms of Arnor

[Gordis]

This thread is inspired by the question in the Appendix trivia.

As you know, there were four heirlooms of the Kings of Arnor that were kept at Rivendell:
ring of Barahir, the shards of Narsil, the star of Elendil, and the sceptre of Annúminas.

Now we know the story, how the Ring of Barahir was saved from the shipwreck of Forochel.

‘But the Snowmen were uneasy; for they said that they smelled danger in the wind. And the chief of the Lossoth said to Arvedui: "Do not mount on this sea-monster! If they have them, let the seamen bring us food and other things that we need, and you may stay here till the Witch-king goes home. For in summer his power wanes; but now his breath is deadly, and his cold arm is long."
‘But Arvedui did not take his counsel. He thanked him, and at parting gave him his ring, saying: "This is a thing of worth beyond your reckoning. For its ancientry alone. It has no power, save the esteem in which those hold it who love my house. It will not help you, but if ever you are in need, my kin will ransom it with great store of all that you desire.�
'Yet the counsel of the Lossoth was good, by chance or by foresight; for the ship had not reached the open sea when a great storm of wind arose, and came with blinding snow out of the North; and it drove the ship back upon the ice and piled ice up against it. Even the mariners of CÃ*rdan were helpless, and in the night the ice crushed the hull, and the ship foundered. So perished Arvedui Last-king, and with him the palantÃ*ri were buried in the sea.' LOTR, Appendix A

So, the Ring of Barahir was with Arvedui during his flight from Fornost, and was saved only by pure chance. But what about the other Heirlooms? How come they were not with Arvedui? Were they held safe in Rivendell before the Witch-King attacked Arthedain? But why then wasn't the Ring of Barahir kept there as well?
And there is this quote from UT

Every king and the chieftains that followed them in Arnor had borne the Elendilmir down even to Elessar himself; but though it was a jewel of great beauty, made by Elven-smiths in Imladris for Valandil Isildur's son, it had not the ancientry nor potency of the one that had been lost when Isildur fled into the dark and came back no more.

So why wasn't this Elendilmir no 2. with Arvedui?