When, exactly, is your DMPC making their moves, if they are not interacting with the PCs (something, which I will point out, the OP assumes will happen regularly)? You seem to be suggesting that the DM spends as much, or more, time playing with themselves than they do with the players.
Yes, they can be making their moves when they are not interacting with the PCs?
Are you saying that DMs spending prep time away from a table is unexpected?
If we steal a page from Dungeon World with its Fronts/Dangers/Dooms, we can even give it a mechanical framework if that helps. But it isn't needed.
You make a Front (a problem or issue in the world), and populate it with a few Dangers. The Front is an organizational method more than anything - a clumping of related Dangers, and a way to say "I want this problem to have more than a single line of events".
Each of these Dangers have Grim Portents and a Doom. The "Doom" is what happens if the Danger isn't confronted. The Grim Portents are the things that can happen along the way, and in a sense expose the Danger to the world (the steps along the way, the side effects, etc).
The Dangers are in a sense Protagonists, as they are modifying the story and the world. The PCs play antagonists, foiling the "plans" of the Dangers.
And while the names are negative, they don't have to be.
Crownless King of the Dwarves is a Danger. He's trying to retake his ancestral home.
The
Doom is an all-out assault by his clan, which leads to the destruction of the people.
Grim Portents could be an initial heroic victory (giving him higher status), a gathering of the clans (legitimacy), a migration (maybe a war or battle with someone who doesn't want a dwarven army moving through their territory?), the retaking of some outer fort (which could be disasterous), then the doom (leading to the fall of the Dwarven nation, as too much strength was sapped by the failed endevour).
Meanwhile, we could have some dark necromancer using that same ancestral home to do something awful as a 2nd danger. A gate to the afterlife, so they can get their lover back? With horrible consequences or costs along the way. Are they using the dwarves as a distraction? Are they in cahoots with the powers that currently hold the ancestral homelands?
Maybe the powers in the ancestral homelands are another danger - but only if they are up to something.
We could add in a meddling 3rd party; say, the ones that will take advantage of the dwarven weakness if they wipe themselves out.
You can sketch this out with dooms and portents, and then have it go on in the background. PCs can interact with it or not, depending on if they care. And you could have a few different fronts active.
In this sense, the protagonists in the worlds constructed story become the BBEG/NPCs. The players can mess with it, or become movers and shakers themselves -- but the DM can't
assume what the players are going to do next. So you sketch your plot assuming they don't do anything, and leave opportunities for PCs to do stuff about it.
The spotlight remains on the players. Table time is taken up by what they are doing.
