I don’t think it will be reasonable to try and pull the same thing off with native tabs. We have to do a whole bunch of tricks to get the title bar to render “normally” when using a themed title bar. We may just need to disable using themes with themed title bars when native tabs are used. The Adaptive theme uses a full size content view to draw the title bar, and normally Apple disables native tabs when using that mode, however I believe if you’ve created the tabs and then switch to Adaptive you can run into this. The project tabs overlap the rendering of the file tabs.
I am in love with this concept and it works well in the default theme, but I think the adaptive theme needs to be updated for it.