Bitpass seems to have a system where you put their code in the pages you want people to pay for - it seems you can charge on a subscription basis rather than a per page basis. I think it would work with whatever open source CMS you prefer as long as you are happy inserting the code. If you sign up with them they have lots of PDFs available about implementing it and about running subscription sites.
I'm not even going there (I'm planning a subscription site too). I'm having two sites - one for just news and the paid one for news, features, interviews, tutorials etc
eta: I read your post wrong, I thought you were going to do 20% of your content free.
Most opensource CMS and blog tools let you post an excerpt, so put your teaser content in that then the full posts will go in a directory which you can charge for using Bitpass and probably other payment systems.