I owned the full package edition on Steam, and I can't add it oh GOG Connect. Not exactly sure why, am I missing a few DLCs that aren't included with the package?

Do you own everything in Saints Row IV: Game of the Century Edition package as that's the version GOG is offering. If you do, it should work. Might have to try few times.For me Connect did not recognize I owned Gat out of Hell first time I tried but when I tried again later it did.

The same as the previous post, but for Saints Row: The Third - The Full Package. If you do, try to contact support and see if they can force check your account.