Peter Jackson aside, my assumption had always been that when Elves shared their thoughts with each other, they needed to be in proximity to each other. Why wouldn't the most powerful of the remaining Eldar want to be able to communicate with each other?
Interesting thought! I think the answer is likely in Tolkien's essay on elvish mental communication,
Ósanwe-kenta. It has been a very long time since I looked at that. It's not in HoME, but in Vinyar Tengwar. IIRC, long distance mental communication was possible, but unlikely. I'll have to see if I can find some excerpts to aid in this conversation.
....And trust the Russians to have the full text of copyrighted material on a website: http://podelise.ru/docs/19345/index-4935-1.html
A legal copy may be obtained for $12 here [it's in Volume 4]:
http://www.elvish.org/VT/shop.html
And indeed the answer is there:
"distance in itself offers no impediment whatever to
ósanwe"
So, if two minds are naturally able to communicate with one another (in the case of Galadriel and Elrond, they are linked by kinship), distance should be no impediment to that communication.
Also from Osanwe-kenta:
Manwe himself said to those who would listen: "Of the Children of Eru Melkor knew less than his peers, giving less heed to what he might have learned, as we did, in the Vision of their Coming. Yet, as we now fear since we know you in your true being, to everything that might aid his designs for mastery his mind was keen to attend, and his purpose leaped forward swifter than ours, being bound by no axan. From the first he was greatly interested in "language", that talent that the Eruhíni would have by nature; but we did not at once perceive the malice in this interest, for many of us shared it, and Aule above all. But in time we discovered that he had made a language for those who served him; and he has learned our tongue with ease. He has great skill in this matter. Beyond doubt he will master all tongues, even the fair speech of the Eldar. Therefore, if ever you should speak with him beware!"
"Alas!" says Pengolodh, "in Valinor Melkor used the Quenya with such mastery that all the Eldar were amazed, for his use could not be bettered, scarce equalled even, by the poets and the loremasters".
I think that this is pertinent to our current plans for Melkor in Valinor.
Eruhíni = Children of Eru = Elves and Men
axan, pl.
axani 'law, rule, commandment; as primarily proceeding from Eru'. Adopted from Valarin
akasān 'He says', referring to Eru (WJ:399).