How would we customize Advanced Search in order to have access to
custom properties we've set up for folders in a list?

The list has two content types -- Folders and List Items. Each has its
own set of properties. If we search for a folder name, SharePoint
finds it, but when we click on the folder listing in the search
results, it opens the folder itself and doesn't provide a way of
viewing or editing the folder properties. Can someone point me in the
direction of what is required to support EITHER drilling into the
folder contents OR viewing/editing the folder properties?