Somewhat late to this chat, but I though of this when the chat idea came up. It should be possible to have a pedagoo post for each chat and embed or better still pull in all the tweets if you use an extra hash tag for each chat, say #sec1, #sec2 ect.
Stuff from Alan Levine’s WP theme might help: https://github.com/cogdog/dailyblank
This would be a space for a longer than 140 char intro to the chat and an archive of the chat itself.