Re: the background...
I like it, simple but gets the point across. As much as I love a well plotted and sprawling backstory I find that short bits that contain the vitals can be great and give you leeway to really define your character on the board.
As far as a couple concepts to toss your way, perhaps the Storm Trooper was the squad commander and successfully completed a mission after the Acolyte that the Inquisitor had paired his squad up with died in the field. A "finish the mission at all costs" attitude could drive him to discover resourcefulness and ingenuity he never knew he had.
This gets him notices, the Inquisitor requests his squads services often in the ongoing campaign and gradually he becomes a trusted pointman. Fast forward and it's easy to see how he could become a more action-oriented acolyte.
The idea that the Inquisitor hides his identity in the field while "deferring" to his acolyte is fantastic. Adds a cool dynamic to any game. I also like the implication that he may be using a basic weapon as opposed to a pistol and CCW (which I feel like is often, but not always, the case).
It would be really cool to see a couple different models for your Inquisitor (Regal mode and Grunt mode). I love the idea of him being viewed more as a blunt object than a nuanced peer by other Inquisitors. Gives him a nice chip on his shoulder but the training to shove his detractors' arrogance down their throats. Great stuff!
Most storm troopers will remain storm troopers for the rest of their lifes, just like most other people in the Imperium. Of course storm troopers are filled with their indoctrination, but so are almost all people in the Imperium, and a storm trooper who, despite all this indoctrination, can still think outside the box would clearly show that most important talent for the inquisition.
I don't see storm troopers as being so heavily indoctrinated that they become soldier automatons. If Space Marines retain enough of their personality to be interesting protagonists (which the Black Library has shown, though I suppose there's room for debate about how much artistic license is taken against canon so that GW's most popular archetype can be written about in a relateable light) then storm troopers who undergo comparatively mild indoctrination should still make interesting and varied characters despite their livelihood.
I actually think that most people in the Imperium are very heavily indoctrinated, they live in a theocracy that represses all kinds of free thought. Those who come from the Schola are even more heavily indoctrinated, they are raised by a church that isn't known for it tolerance of free thinking. Of course, Imperials are still people, it's just that most of them are religious zealots by our standards, they live for their Emperor. There of course also are those who are depicted as even more religious than the rest, and are seen as zealots in the setting, but we should bear in mind that Imperial society knows little free thought and is very, very repressive.
I totally respect that view and think it's 100% legitimate. I tend to prefer the view that while there is a veneer of piousness across the Imperium that many average Imperial citizens (while they are staunch believers) will still be more concerned with where their next meal is coming from as opposed to saying their prayers to the Emperor on all the odd hours of the day.
My main point being that I tend to view the Imperium through the lense of "repressive Theocracy can only go so far." Much like modern day repressive regimes they may project an image of absolute conformity but this is far from the truth. It is totally fair to counter that in the 41st century daemons, aliens and Chaos are real physical threats that engender greater degrees of loyalty and piety as a matter of survival, I just find it a more interesting place to imagine that the indoctrination, while significant, is not as all-consuming.
Again, both views are totally valid and I'm not trying to argue that mine is the one that should be adopted, just trying to explain where I'm coming from. Additionally, no two planets are exactly the same so there are certainly cases where I'd adopt your views in terms of the strength of Imperial indoctrination.
I hope that makes sense, interesting discussion regardless!