Great. Going through the site — perfect. A lot of people focus only on SEO and don't write naturally. It ruins the entire reading experience. You have the opposite problem (good content - and less focus on SEO). And that's great.
The above method - to "sprinkle" keywords should be good enough. Other than that, as I quickly glance:
- Tighten your menus (less the better)
- Find popular pages (and categorize them). Make them into a cluster.
- Add breadcrumbs (above the headline)