To extend your thoughts, another important form of giving is the giving of one's self--self-sacrifice, but the giving of one's own innate powers and essence to others.  The creation of the Valar involves the giving of some of their essence to Arda (Yavanna with the trees, for example).  We then have those who surrender their powers or essence to others.  Earendil sacrficing everything in journeying to Valinor, Gandalf sacrificing himself, Frodo giving himself, Arwen giving to Frodo, all of these acts are related to the giving of tangible gifts.  Gifts might be tokens of exchange in symbolic economy as you very aptly put it, but the ultimate gift in Tolkien is of one's self.

I also tend to think that Galadriel is giving in the sense that she is trying to maintain one little corner of Arda unmarred in Middle-earth.  She's following the example of Melian and Thingol in cordoning off their realm in order to keep one part of the world free from taint.  This can look a bit "selfish" from one vantage point, but in the larger picture of how Doriath and Lothlorien are realms that preserve the essence of Middle-earth that existed before the taint of Morgoth stained it, their work is trying to keep at least one realm pure since they cannot cleanse the whole world.  Certainly her gift to Sam is part of her recognition that Lothlorien is at an end (with the loss of Nenya's powers), so it does represent an effort to continue preserving something "like" Arda unmarred, even if it is only a single mallorn west of the Misty Mountains.

      
Not to be bested, Saruman gets his own portrait icon