I realized that it may not be immediately obvious to everybody how you can customize the MOSS Search Center to add the Live Search Web Part I blogged about. It is really very simple.
The Theory: all you need to do is to create new "Live" tabs on the Search Center (one for Search and one for Results), plus the corresponding "Search" and "Results" pages (all from the Web interface). Don't forget to modify the Search Boxes to point to the corresponding new pages. Then, you just import the attached Web Part on to your Results pages, and it will automatically use the current query and display the results in the Search Center.
The Practice: here's a quick screencast that shows how to do it: configuring the Live Search Web Part on screencast.com!