How to Move My Library to a New Location

The title is a bit misleading. This is actually related to a previous discussion I started but never got any feedback on.

Here is the situation:

I have iTunes Match.

For whatever reason, my iTunes library got hopelessly muddled and confused. Probably user error.

I decided to move the library to a new location (different external hard drive).

I completely uninstalled iTunes and all Apple software from pc. (yes, i have a mac but easier to keep this on the desktop).

I reinstalled iTunes, but something is still there, because my library immediately showed up. I turned off iTunes Match, updated the preferences to point to the new location and turned iTunes Match back on.

iTunes does not "see" my new library location, and tells me that all music is only in the cloud.

How can I make it re-scan the hard drive and recognize that the music is all there?

The big problem this causes is that, as I add music, it's impossible to tell what is really physically there and what needs to be downloaded.

Thanks for any suggestions or help. Perhaps I need to uninstall in a more thorough way, if so, I welcome help with that.