I've been thinking about this idea for a while and love the reimplementation idea. I really want to start live-streaming myself coding (or pair programming) and have been trying to come up with some ideas that would end up being interesting to watch.
One idea was taking a popular open source tool with a good test suite and trying to get the tests to pass, but I think checking code out at a point before a new feature is implemented and reimplementing it could end up being really interesting. Could even make it more interactive by sharing the checkout point so viewers can do an implementation themselves and doing a stream walking through different interesting implementations.