To be honest, based on the video we see when we decide to free the Overlord, it can be said that the son welcomed his father with open arms, and he is unlikely to set any conditions for his release, let alone overthrow him and usurp power. So, we can initially show Kha stepping onto the land of Ashan with a retinue of several legions of demons, but then something happens, and the demons are forced to postpone their attack on Ashan. I think that "something" could be the appearance of the Order of the Void, which solves the problem of the annoying demons in a well-known way. The demons retreat to Sheogh, and in addition to seeking revenge on all of Ashan, their goal will also be to take revenge on the Order of the Void (we have three opposing sides: demons, voidlings, and the Alliance). In this way, we won't disrupt the lore too much, and we'll create the necessary conditions.

Added 30 minutes ago
So, at the beginning, we can play either as the Overlord, who, having been freed from his shackles, invades Ashan with an army of demons, or as the leader of the Order of the Void, who, with his army (void spirits or whatever you have planned for the void army), attacks the demons. At the end of the scenario, the Overlord and his army of demons will be forced to retreat to Sheogh.
In general, this is probably nonsense, because the ending of Dark Messiah is not specified, and the dubious comment that we are currently relying on is extremely implausible (I'm talking about the comment that Saref freed the Overlord and the Order of the Void appeared, etc.).

After the death of Arantir, the Order of the Void will seize power in Erathia, and then the undead will have a campaign to capture the Silver Cities.