A discussion board seems to me like a very strange place to have that kind of rigorous discussion. It seems like it belongs in a wiki (or similar) where only the talk/discussion page has historical arguments, counterarguments, and contextual comments, but the main article is just the finished argument. I find it hard to follow a discussion thread where individual portions of an argument appear in different comments (sometimes entirely different articles) with little or no context. Perhaps I am misinterpreting the degree to which you think extraneous comments should be excluded. Or perhaps there is too little re-posting of improved arguments once the discussion has finished. Or too little use of the existing wiki.

The best example I can think of is the metamath.org proof explorer. It's composed mostly of rigorous derivations of theorems that (conveniently for mathematical arguments) can be checked for correctness by a computer, but with clarifying comments where necessary and a history of abandoned theorems and definitions with explanations.