First, go to Preferences > Advanced, and uncheck "Copy files to iTunes Media Folder." For whatever reason, that seems to be necessary to get it to search for missing files. You can re-check that option when you're done.
You have to get iTunes to recognize that tracks are missing. The only method that I know works is to select the first track, hold the down arrow on your keyboard, and scroll all the way through. This should check each track as it is highlighted and mark it with that exclamation icon.
There may be a better way to do that…
Once iTunes recognizes multiple tracks are missing, select one, and get info. It should notify you that the track is missing. Find the file for that one, and it should then ask if it should search for other missing tracks in the same location. It may take a long time, depending on how many tracks it has to go through. Just let it churn away and it should eventually come up with a message saying "X items were found, X items could not be found," or something like that.
I've done this many times, moving old items to a network storage drive. Works with music, podcasts, books, audiobooks, music videos, and mobile apps.
Best Answer
Pulling down the comment above, since it satisfactorily answered my question, and it seems this question will not be receiving more activity anytime soon.