Thanks for your post!
The head is actually angled backwards by 10 degrees but not visible very well in the photo. I've attached a better picture to this post, you can clearly see the difference in angle between the two sections (neck and pegbox) - the mathematics check out.
I'm an electric bass-player so my design is based on a 3-stringed hybrid of an electro-acoustic bass (ovation style) and an orchestral upright bass, so it will have a double-bass bridge. I'm not sure if I'll need a bass bar however, since the resonant cavity is huge and I think the hardwood ribs will suffice. As you quite rightly pointed out, it has a sound post (1.5 inch wooden dowel) which will probably end up being glued to the face-plate.
Since you're a fellow engineer I'd be happy to send you the technical drawings via email (don't want to share them here yet) and would welcome your advice since I'm really just making this up as I go along.