Human brains are not - and let me be completely clear here, not even a little bit - like computers.
(And before anyone complains, I'm not the one that tagged this as neuroscience!)
Computer hardware is standardized, logical and rigidly structured. Given a sufficiently high-resolution picture of a CPU's silicon a skilled engineer can tell you what each part does just from the interference patterns at low magnification and at high enough magnification they can reproduce the actual circuit that's printed on the silicon die. An acquaintance of mine a few years ago was a silicon engineer who worked on CPU designs for most of his adult life and could tell you the make and model of any CPU just from a scan that fit on a normal computer screen... and give you a 3-hour lecture on what was wrong with the layout.
Meanwhile, the top 10,000 neuroscientists on the planet can't tell you what any particular neuron does, because that's not how brains work. Rip a neuron open and study the chemical structures in it, you'll still have no clue what that particular neuron had stored in it. Even if you could map every single neuron and synapse (we can't, but imagine that we could) you'd still not have a functional simulation of it. The largest successful whole brain simulation ever created was of a caenorhabditis elegans roundworm with 302 neurons and only 5,000 or so synaptic connections. While we can simulate these things at almost real-time now, we're still missing a lot of information that makes them less that perfect. In 2013 they managed a simulation of ~1% of a human brain (they had 1.73e+9 neurons and 1.04e+13 synapses in the simulation) at around 1/2,400th real time... but I'm sure they've made it a lot further since then. We've almost managed to fully model a larval drosophila brain in the last few months, with the same lack of detail that the roundworm simulations suffered from but a lot more spackle over the details.
(No, Spaun is not a whole-brain simulation. It's good, but it's far too high level to be a true sim. It's about as accurate as a 50x scale mechano model of a human hand.)
And to top that off, brains are delicate as all hell. Disrupting communications between a handful (like the number, not the amount of neurons you can hold in one hand) of neurons can cause catastrophic failure of the entire structure. Quantum tunneling isn't going to help you here. Oh, and the brain state changes significantly due to microscopic changes in chemical balance. Tiny changes in hormone balance can flip a brain from perfectly normal to homicidal rage in seconds. Toxins produced by your own glands can screw with your memory and perception. And of course some brains are prone to all sorts of tomfoolery, like cascading feedback loops in epileptic brains.
And finally, no two brains are alike in any but the broadest possible strokes. Even with FMRI and all the other fun toys we've developed, our best guesses at the moment still require neurosurgeons to prod bits of the brain and see what happens. Or at least what the person who is awake while they're doing that reports. "Oh, you lost vision in your left eye and now you're tasting colors? That's unexpected." is not the sort of thing you want to hear from the guy who drilled a sodding great hole in your cranium a couple of minutes ago.
So yeah, your demonic forces are great at working with knowable systems like sub-micron silicon, but even simple brains are orders of magnitude more complex. Human brains? 86 billion neurons. 600 trillion synapses. And we have no idea how most of it works.
Computers on the other hand are easy to subvert... but also easy to protect against that subversion. Forget making them smarter, make them robust. Build analog computers for specific tasks that are faster and more robust than any digital computer. Build big, chunky circuits that couldn't care less if a few thousand electrons get displaced all at once. And don't make one, make ten. Get them to run calculations independently and make sure they all agree on the outcome before you trust it. If the failure rate is high, scrub them all and switch in a whole new compute bank.
Because if you rely on squishy meat to plot your hyperspace injection metric, you're doomed. Especially if that squishy meat is hooked up to a delicate piece of electronics that can be subverted.
Meanwhile, every part of your ship is managed by fallible electronics that the demons can apparently interfere with. Life support is quite important. So are the various doors between you and the Big Empty. I imagine the reactor control system is pretty important too. Nice drive system you've got there, it'd be a shame if someone tweaked the cycle timing on the plasma induction manifold. You didn't need that anti-matter containment field did you? Oopsy.
Oh, and all that computational gymnastics you've trained for since conception is cute and all, but those sensors you rely on look kind of hackable from here.
The scenario you've detailed makes it basically impossible to do anything that a human (or group of humans) can't manage by hand. That counts out a lot of existing tech and vast swathes of the tech we take for granted in most science fiction.