I had a similar thought, but on a different tack.
See, this whole farrago reminds me of the "The Ship" thread, in that (at the very beginning, at least) the idea was that the threat to the Imperium came not from the possibility of success but rather from the sheer cost of redirecting resources from worthier endeavors to try, including the production of conventional armaments. It would also be vaguely reminiscent of Mao's Great Leap Forward in execution, with psyker canning equipment taking the place of backyard blast furnaces but similar underlying psychology: that any discrepancies between reality and the grand plan are someone else's fault, and as the fault lines between the two grow it's best not to be visibly unenthusiastic, lest one become the next scapegoat. The Great Leap Forward actually inspired Paranoia's Wholesome Meal Distributor adventure, which can give us a template.
I'd do it as a Mechanicus project, so the acolytes (who are Ordo Machinum) need to tread carefully vis-a-vis Inquisitorial power, and have them called in by a Magos Logis who's alarmed at the actions of her forge world's new Fabricator-General, having been schoolmates with him decades ago before he was repeatedly disciplined for minor insubordination and ultimately exiled to run the waste disposal system at a pedanticum complex or some other dead-end make-work job. Despite having never actually achieved anything -- those records are currently sequestered, but hey, they're talking to a full-blown Lexico Arcanus -- somehow he's running the planet now. Moreover, he's running it into the ground with an iron fist, talking about how the hidebound old hierarchy needs changes if they're ever going to get anything done and he knows just where to start. Production is flagging, quotas are barely met, dissenters are disappearing and if something isn't done soon, someone with a lot less capacity for subtlety than the Inquisition is going to come knocking with power-armored fists asking where their bolter shells are. If he's anything like she remembers, the new Fabricator-General is likely to react in a way that ends with the world in flames, so maybe the acolytes can get to the bottom of this and find a way to restore normalcy while there's still a forge world to fix.
Then, of course, the question becomes not only what he's up to, but how the normal Mechanicum hierarchy was so thoroughly broken as to let this happen; the reach needed to find the only sub-techpriest who wouldn't question being suddenly handed control of a planet and then to actually make that happen is staggering and implies corruption on up to the sector level. It's an opportunity to show off how the Mechanicus and by extension the Imperium, for all its flaws, does generally work, by showing what it looks like when it doesn't -- and how a sufficiently rigid hierarchy can be made to do insane things when the alternative is being destroyed. Have the stakes get higher and the projects get wierder ("Are you suggesting we can't make low-priority Titan parts entirely out of worn-out servitor wetware to reallocate metal toward more important projects? Have you so little faith in the New Mechanicus?") until finally they discover the psyker-canning facilities dotted around the planet desperately trying to mass-produce MIUs with AI-that-isn't-AI monitoring systems that will run for decades and just stuffing badly-cloned brains into jars so they have something to show when they get inspected.
Ultimately, I'd have it turn out so that this entire thing was a mistake, the result of an unintentional three-card monte between multiple conspiracies who kept swapping out each other's patsies right on up the ladder until this happened and who are now already at covert war with each other over it, while at the same time the new Fabricator-General is conducting his own private inquisition to quash dissent and attracting more plots to remove him by the minute. Lots of Mexican standoffs, but with more guns pointed at more people by virtue of the participants all having mechandendrites. Some important things -- or people -- hidden piecemeal as/in servitors. Heck, high-ranking magi hiding their brains in the psykercans. Fights in forges dripping with molten metal and increasingly on fire, or in cyberspace/the noosphere. Have one of the magi try to use tons of Ork spores to psychic-gestalt the psykercans into operation with predictable results, along with the appearance of some Eldar and Chaos cultists who have thoughts about these billions of mass-produced psykers they've heard so much about. Let that whole "The Emperor is not the Omnissiah" thing pop up and start a mini-civil war just as extremely ticked off Black Templars start asking why they haven't got any new bolter shells. Have someone pop open a long-sequestered can of Obliterator virus in a last-ditch attempt to bring this much-vaunted psychic superweapon online by the cyborgiest shortcut available, because goodness wouldn't it be handy with everything going on.
Getting the planet back to normal from there would be one heck of a story, I think.