Proposition.

to overtrain the skill/procedure/process/routine
I am not sure if this sounds well for an Englishman, let native speakers correct me.

Russian term (edited): надо довести до автоматизма

... has to practice xxx before it gets (entirely) automatic (and ingrained)

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Note added at 2 час (2020-06-17 15:19:02 GMT)
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All you need to do is focus hard on your mechanics, and then just let the ball go. Once it gets automatic, you won't even think when you get ready to throw it.
https://books.google.by/books?id=MuGrDwAAQBAJ&pg=PT78&lpg=PT...

Developing habits is a difficult task. In the beginning, you’ve to work hard every day to perform a new habit. Once, you repeat the habit for one month, you find yourself performing the new habit is easier than before. Practice the same habit till it gets automatic.
https://positivelifeproject.com/increase-daily-productivity-...

During training, Sherry said, she worked on techniques that eventually helped her overcome the fear of competing and instruction.
"We would develop strategies for different scenarios: 'Okay, how am I going to come back if someone comes at me with this sort of technique?' You practice that over and over so it gets automatic," Sherry said.
https://www.theeagle.com/news/local/bryan-couple-wins-taekwo...

Now here’s the trick.
Think of those at the same time, AND add to that the decision you feel guilty about. Hold all 7 in your mind.
That is a neurological way to “get perspective”. You literally connect “good decision neurons” to these “guilt neurons”.Like most of my mind hacking members, this will probably be the first time you try something like this.You won’t do it “perfectly” the first time, but it gets automatic REAL FAST.
https://medium.com/the-ascent/7-steps-for-a-guilt-free-2019-...

Согласно большому толковому словарю русского языка Ефремовой Т.Ф. автоматизм понимается как абсолютная ОТРАБОТАННОСТЬ действий или движений, достигающаяся МНОГОКРАТНЫМ повторением, ТРЕНИРОВКАМИ. Теперь открываем статью на blindfold, например в толковом словарь Коллинза, и читаем: If you say that you can do something blindfold, you are emphasizing that you can DO it EASILY for example because YOU HAVE DONE it MANY TIMES BEFORE. Характерно, что вариант do smth blindfolded встречается чаще словарного.
Для второго предложения я бы предложил выражение get или acquire the knack of. Например, Have soldiers train hard to get the knack of setting up their equipment (quickly and easily prior to combat).

I think this should sound good in the military context.

"Fitts (1962) postulates three stages in motor-skill learning: cognitive analysis and verbalization of what is involved, so that the learner understands what to do; fixative, involving practice to the point of competent performance; and autonomous, involving further practice to the point of automaticity."
https://bit.ly/3fxBHo9

"When practiced correctly and in sufficient volume, the technique should build reflexive reactions that a Soldier applies in response to a set of conditions. Only with correct practice will a Soldier create the muscle memory necessary to serve them under conditions of dire stress. The goal is to create automaticity, the ability
to perform an action without thinking through the steps associated with the action."
https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN5846...