Thanks for the kind words.
The demo version and full version are separate apps, with separate settings and a separate database. However, by default they share the same book folder (Calibre_Companion).
What I would do is backup CC's settings in the demo version, install the full version, then restore the settings into the full version. Connect the full version as a wireless device. CC will attempt to match the books in the book folder with those in the calibre library. Resend any that that the matching process gets wrong (this happens a lot for formats other than EPUB).
Once you are content with installation of the full version you can uninstall the demo version. This will not delete your books, but it will clean up the space used by the database and the app itself.