What information has survived the longest? Perhaps the information encoded in DNA. But, to survive in harsh environments with the constant threat of destruction, new copies are made continually within cell nuclei.
Which leads to my suggestion. Maybe we don't just want our data preserved for millenia, we want it made better! Thus we should initiate a process of artificial intelligence, seeded by our own ideas but with freedom to innovate in years to come. Then, it can adapt in order to communicate with any future would-be readers.