The catalogue system has not changed for years.
In your first post "When I try to import the HDR files from the folder in which they reside, LR won't import them." Any error message or are they just dimmed out? The latter would be consistent with "Many (but not all) of the HDR files, and an occasional image edited in Photoshop, are showing up in the LR Library in completely separate folders, outside of any master folders."
Physically, where are the originals? Are we talking Mac or Windows, internal or external drives or network or whatever?