I'm still a bit suspicious about abstraction leaks in the concept of "save this session." I'd prefer to think in terms of a library pastebin, where I may choose to turn my REPL session into a library but I'm not misled into thinking it'll preserve more about my session than the raw code I entered.
For what it's worth, managing user logins and passwords is a very easy business with WordPress! The challenge would be figuring out how to interface those WordPress user accounts with REPL functionality.