Well, the main problem is that sections aren't editable easily, i.e. they aren't editable at all.
Did you try just to fill new articles with premade contents? I admit that I don't know much about programing but the process I see in my head is:
1. Admin or users with enough rights create template with some text (of course, text can have BBcodes in it, but BBcodes are just text before they are parsed).
2. User in process of creating article chooses first which template (kind of template I'm speaking of) to use, or not to use any (create blank article).
3. This text is just copied in a new article, but it's just plain text (at least from programs point of view, never mind that it has BBcodes in it). As I would paste it from somewhere else, I think you could program somehow that text would be inserted in article. And not some object, code construct, just plain text.
4. User fills that text with contents, as users do.
5. When user saves it, text gets parsed, as usually.
6. Now we have wiki article with working template, correctly parsed, someone else could edit sections and whatever else.
I think the key is that you treat my kind of template as plain text whole time and let parser do it's magic when time for parser to do its magic comes.
As I said, I'm not a programmer, but that's how I see it and I think that there are ways that enable you to put some predefined text (of course, admins and users with sufficient rights are responsible for text's meaningfulness) first and let parser to create wiki article later.