Maybe "Tree of Love"...(bit like a family tree) a firmly rooted, spreading tree, the members represented by the branches, the leaves heart-shaped representing the gifts....Your post reminded me of the Shel Silverstein poem "The Giving Tree", but I don't suppose you could use that as there would probably be copyright issues. Anyway...that's my suggestion (a little out there, but I think I'm among friends here!).
If this group was local to me - I would join in a heartbeat.