Re-connect iTunes library from different drive
The easiest is to start with a fresh and empty folder in the new ~/Music directory.

Fire up iTunes and tell it to use the media folder on the the external drive and quit iTunes after making whatever settings you want about copying files / organization. I would recommend leaving both selected.

Then move just the artwork folder and the itdb / xml files into place and replace the "empty" files that got created on the local ~/Music/iTunes folder. (basically use Finder to move everything back except the folder containing the media.)

When you start iTunes it should run a quick check to make sure all the files are working and you can proceed with your app management / music enjoyment.