There is now a way to upgrade the game on GOG (the Larian Vault download was a quick fix until they got the details sorted out). From the GOG DC release topic:

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Anyone who backed the Original Sin Kickstarter and claimed his or her copy of Divinity: Dragon Commander on GOG and *didn't* get the Imperial Edition code issued, please contact [GOG] Support and we will give you a free code for the DLC. In the subject of your ticket, please put, "Imperial Edition Upgrade for Kickstarter Backer".