I did some further exploration and testing on this. I first changed my Preferences to store new media in a different location, my new external harddrive. Then, I copied (not moved) all of the files from the original location's Music directory to the Music directory of the new harddrive using 2 open Finder windows. I then started Music and attempted to play one of my CD's. It indicated that it could not locate the first song/track and asked I wished to search for it. I let it search. It found it in it's original location and apparently changed internal pointers/indexes to the new location. It then asked if I wished to locate the remaining tracks/songs, which I did and those were changed as well. That CD now plays from the new location just fine.
I tried this same process for a 2nd CD with a minor exception: rather to play the CD at the Album level, I selected the 1st track individually. It again indicated it couldn't find it, I let it search, it found it and changed the index for it. However, the exception was that I never was asked to correct or search for the remaining tracks/songs from the album. I didn't try to play the entire album to see if it came up then, however, I just selected each track, 1 by 1, and let it resolve individually. So I guess this is resolved but maybe the instructions/steps for doing a move could be much more clear, concise and understandable to people of all technical levels. Just a thought. Thanks.