With a width-constrained content panel in the static documentation site, you can end up with a large, empty, white "wing" on the right of a wide window. We should mitigate this effect by floating the (still width-constrained) content pane in the center. At the same time, doing so can add a significant separation between the page-level ToC, which is currently embedded in the navigation rail on the left, and the content to which it relates. So we should extract the page-level ToC into a small box to the right of the content, that floats with you as you scroll down the page (i.e. it never scrolls out of sight). It should retain the current "you are here" behavior.
When the page is too narrow to display all three panes (navigation, content, ToC) the ToC should disappear (move to the bottom?) rather than overlapping the content.
An example of the width-centered content can be see in the Atlassian Personality guide
An example of the always-with-you page ToC can be seen in GitHub's Git Handbook.