I do not think it is fair to say that Galadriel does not miss Beleriand very much. True, she did leave Beleriand before it was destroyed. But as you point out, Elves have perfect memory. She remembers Beleriand clearly, and now it is gone. Her final farewell to Treebeard references their time there:
As for Galadriel's relationship with Valinor...in at least some versions of the story, she considers herself to be still under the Ban. Even in the Third Age, elves may go to the Grey Havens and take a ship along the Straight Path to Tol Eressëa. And yet....it is not until she tells Frodo that she will diminish and go into the West that that path becomes one that she might take. The song Námarië is in Quenya, it is a song of the Exiles (Noldor). And Tol Eressëa is not Valinor. Permission to return to Tol Eressëa is not permission to enter the Blessed Realm.
"It is sad that we should meet only thus at the ending. For the world is changing: I feel it in the water, I feel it in the earth, and I smell it in the air. I do not think we shall meet again."
And Celeborn said, "I do not know, Eldest."
But Galadriel said, "Not in Middle-earth, nor until the lands that lie under the wave are lifted up again. Then in the willow-meads of Tasarinan we may meet in the Spring. Farewell!"
As for Galadriel's relationship with Valinor...in at least some versions of the story, she considers herself to be still under the Ban. Even in the Third Age, elves may go to the Grey Havens and take a ship along the Straight Path to Tol Eressëa. And yet....it is not until she tells Frodo that she will diminish and go into the West that that path becomes one that she might take. The song Námarië is in Quenya, it is a song of the Exiles (Noldor). And Tol Eressëa is not Valinor. Permission to return to Tol Eressëa is not permission to enter the Blessed Realm.