Add categories and posts to page hierarchy

Question

So, I find myself in this situation now and again, trying to solve a particular workflow. I have a page hierarchy something like this:

Page 1
    Sub-page 1 (category term listing)
        Post 1
        Post 2
    Sub-page 3 (standard page)
Page 2 (category term listing)
    Post 5
    Post 6

Now the particular problem is that I want to maintain this hierarchical structure, particularly in the breadcrumbs and url (friendly rewrites). Basically I want category and post pages to appear in the page hierarchy, for example /Page 1/Sub-page 1/Post 1/, rather than the wordpress default: /category/{category-name} and /blog/{post-name}.

Is this just something WordPress won't do, or does anyone have any clever workarounds?