I did answer your point. Extremists are not likely to get enough support to get on the ballot, therefore no public financing. Tea Party? Probably, and that would be good. Instead of pulling the R's hard right, they would have their own platform and candidates. Greens? Maybe, the Dems worked hard to keep them off the ballot here in Ohio. Unfortunately, incumbents make the rules.
As far as spending other people's money, air time should be given as the bulk of financing. There would still be additional donated funds, of course. But I believe cutting corporate influence would actually be cheaper for most people.
The instant run-off works like this - you vote for a first and second choice. If no one has a majority of first choice votes, the top two candidates run-off including second place votes.