Turns out there is a way for the people in Aman to "communicate telepathically with Cirdan"! One of the Palantiri, the Master-Stone, is held in Tol Eressëa in Aman. Anyone with access to it can presumably contact those who hold one of the other Palantiri, and there definitely were Palantiri still in Middle Earth in the Fourth Age.
Big caveat: there's absolutely no indication that this is how the Eldar communicated to Cirdan than Samwise/Gimli will be allowed to go to Aman, and there's no indication either that Cirdan even had one of the Palantiri,* but it's conceivable.
As for why Eärendil and Amandil needed to cross the sea to talk to the Valar: Tol Eressëa isn't in Valinor, and the Valar don't live there. Possibly the Valar didn't actually have a Palantir, so the only way to talk to them would be to visit them directly.
*Cirdan did have access to the Elostirion-stone, but this stone was brought to Aman by the White Ship carrying Gandalf & Frodo/Bilbo.