Is there a reason why the site is so Parent / Top heavy with the navigation? If each piece of content is to be part of many different categories (parents), I wouldn't completely dismiss breadcrumbs altogether.
You can consider creating a dynamic breadcrumb which tracks the route that the user did take. Each node in the breadcrumb can also be a dropdown that links to other parallel pages in that level. This way it's an adaptive historical view.
The breadcrumb could display smartly based on the page levels within the site, and not just take the browsing history.
If the user went: ANOTHER PAGE > HOMEPAGE > PAGE 2 > HOMEPAGE > PAGE 4 > PAGE 5
It would set the pages up as separate branched breadcrumb.
If on PAGE 2, the breadcrumb would be: HOMEPAGE > PAGE 2
If on Page 5, the breadcrumb would be: HOMEPAGE > [PAGE4 v] > PAGE 5
Whereby Page 4 is a dropdown with parallel pages.
Having an Anchor like the Homepage will help to orient the user.