I've ALMOST managed to do this already using the NodesAsTabs addon...but only almost. What I have now is a new tab that goes to a category with its own page. However, I'd like the new tab to display SEVERAL categories, just like the main forum page can.
Theoretically, if it was possible to embed categories in a xenforo page node, that would be almost perfect. All that I would need at that point would be to figure out a way to stick the sidebar in.