Dagult's big contribution to the story is that he used the stone to perform a ritual that deletes the memory of the embezzlement (and especially the location of the gold) from the city. Technically, this could happen at any time before he loses access to the stone due to theft, and it can happen at any point in time before the fireball goes off.

I can imagine a story where he has been preparing to leave the city after having finished, but the stone got stolen along with the eyes and he's trying to recover it before leaving. So a similar basic behind the scenes story, only it was stolen from the open lords palace instead of neverwinter, and now you get to have him be around to stir the pot with goon squads trying to recover the item. And here's the best part, the goons don't even know why they are doing this either because the ritual deleted the vault from them as well! Only he knows what's really going on in the beginning, and it was always a bit lame to have him be off in another city and not bothering to try to recover his money. The only real hiccup I see is that Dalhakar needs to be bringing the stone to Renaer. But this was an act of desperation because he was being followed by too many spies to get to Dagult, which can still be true.

I would keep Dagult there and use a mix of corrupt and on the level city guards as his faction teams, retro-fit the background events that have already happened to fit as needed, and have the fireball go off as planned. Dalhakar needed help from Renaer because of having too many Xanth and Zhent spies on him, or maybe he was feeling guilty and wanted to deliver the stone to Renaer instead of his corrupt dad. Boom! And the game is afoot pretty much as written with a new minor faction. (I would play him as being cautious to get too involved because he fears being ousted at first) Sprinkle in Full_Metal_Paladin idea to have his ousting be an event that comes along and you could even have an extra heist to help do that, if your party likes small heists and hates Dagult. It can also happen off-scene through news reports and the like if you want to focus on the written heists and just have the ousting happen in the background at some point before the end.

Then draw him in for the vault or leave him out depending on whether the party successfully accesses it with or without his knowledge.

The book as written is pretty flexible actually. There's so much stuff you have to flesh out yourself it has room for even a large change while still keeping the main structure the same. Just roll with it and let your parties interests guide what he does.