Could try for more specialized servant types? Like in general. For example while Cyber Skeletons are useful if you need to shoot things, craft things, or just need someone with a pair of hands, they're not great shooters or crafters. Could have slimes who's purposes is to provide more specialized minions to suit more esoteric needs that aren't explicitly covered by existing minions. For example, fire-proof minions to deal with extreme heat areas.

Their factory function would basically be built around tinkering with minions. While every factory can create their own, your factory is where the original creators would build and test out new minions before ported them to their respective factories for production. In the new world, this could possibly be expanded to take new denizens and see what abilities they have could be adapted into minions or even the Overseers themselves.