JClosed: Just an idea, but if you go to your game library on this website, you can download the off-line Deluxe Edition upgrade installers. They are the two files at the bottom of the download page.
It would not surprise me if you can use those installers to upgrade your on-line installed game. If the installer cannot find your game directory, you can point to that one in the installer front end.
When the on-line update drops, it probably overwrite those files, but then you have the upgrade "officially" installed using Galaxy.
Those don't show in my library, or else I'd have tried that. I've looked in all the places they are supposedly available and so far the only place I can get it is by purchasing it. Hopefully this is a solution that can work for someone else.