The result was window.js, a tiling manager for web sites. We hooked it up to our existing visualizations, did a bit of server-side magic to allow saving and loading, and voila-- 100% configurable, resizable, and sharable dashboards.
Check out the live demo here!
A side note:
As an engineer, there are some things in here I'm not proud of. I didn't quite grok data structures when I set out writing window.js, nor did I quite appreciate the full breadth of functionality of the modern DOM.