I use MTU Hoster and I have transferred it several times in the past. Here is what I did.
I have all my songs in a single folder. I have ripped all my CD+G and have not purchased any online but I believe the procedure is the same. I copied the folder with the songs to another external drive (much faster than using my NAS). If you are using the latest version of the Hoster or Hoster Lite Duo (not Hoster Lite), you can install it on two machines. I usually use the second license to install to the new machine. Otherwise, you have to run the Hoster Installer and deactivate the license by uninstalling the program and install it on the new machine with the serial number. That will reactivate the license.
After the Hoster is installed in the new machine, I copy over the folder with the songs. Then inside the Hoster, you can rebuild the database on the entire folder and you are good to go.
I just found a page on MTU's web site on how to do transfer license
here. Good luck.