There may be another alternative to cryonics that doesn't require a Big World - indirect mind uploading (scroll down to "Using ‘indirect mind uploading’ to avoid staying dead"). The idea is that if you record every second of your life (e.g. on video), using this information a future AI might be able to converge on a specific brain configuration that is close to your original brain. Since only certain brains would say, write, do or think (although we currently can't record thoughts) the things you recorded yourself saying, writing and doing, depending on the amount of information the AI has about you, it might be able to narrow it down and the scenario becomes similar to Yvain's 'gradations of identity' scenario in this post.