I am keen to do similar things myself. Have you played with the page controls export as static html?
If you do something in your own button and filter the saved tiddlers. You could be on your way.
In my own experiments I was happy to export every tiddler as static html page but the default as on tiddlywikis.com/static pages the link from one tiddler to another goes to other static pages.
As I result I played with the template used for static pages with some success.
I am keen to have a parallelle html static site internet facing to support seo that loads quickly but on click loads the interactive wiki with a splash screen.
Later I would just like to exportchanges only.
Regards
Tony