While I don't have any ideas for how to archive the tweets (presumably there's some progam that can archive by hashtag?), my best suggestion for conserving the whole thing is, ironically, displaying them online. If you could divide tweets by episode and convert them into individual pages, then have simple links between episodes (and a master list), it would be really neat. I don't know where you would host such a thing though.

Kudos for all you've done on this!