Pandora's dilemma definitely reminds me of Ashildr, from Doctor Who, a Viking girl who became immortal sort of by accident. Infinite lifespan, finite memory. She started keeping a journal with the most important things in her life, to re-read when she had forgotten who she used to be. It filled a respectably-sized library in her home and spilled out into the halls the second time the Doctor encountered her. There were places pages were stained with tears, places where pages had been torn out because she wanted to forget what those pages held. But she only knew what was in the diary as something she had read about. One wonders whether someone like that could actually learn the important lessons in life, or whether they too would be forgotten along with the details of how they were learned. Apparently she could, though, because the person who the Doctor met at the end of the universe was very different from the girl he saved from dying.
They did something visually similar with Methos's diary in Highlander, kept since writing was invented, with parts of the diary on papyrus scrolls and cuneiform tablets. In that series, however, Immortals have excellent memories so I never really got the impression Methos needed the diary.
From what Pandora and the Emissary of Magic said, it sounds like an Immortal only passes along what the most recent incarnation chooses to pass along. There isn't an ever-growing library of mental tomes. Or, if there is, the older ones must be much harder to access than the most recent one. Perhaps they're nested, like a hard drive archive with files for a previous archive that contains a previous archive which contains the recovered files from a crash which contains.... Hmm, wasn't there an xkcd on that? ....yup, there sure is!