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Geoffrey Perret is a British national who came to the US, went to Harvard, and enlisted in the US Army. Subsequently, he wrote a couple books including (I think) "A Country Made by War", and (definitely) "There's a War to be Won".
I recommend the second book, which is more of an organizational history + account of the rapid build-up around WWII. Aside from the usual campaign history in the European theater, there are separate chapters on (inter alia) the all-black combat regiments that were explicit 'social engineering' of a high minded kind by Gen. Marshall; women in the army; and Asian-American combat regiments, which are worth the price of entry alone.
I recommend the book because inside it is, I think, an answer to your question of whether there could be a mission-focused civilian institution that possessed all the character-building virtues. Perrett says a great deal about the Civilian Conservation Corps and how those who had served in the CCC formed the basis for the NCO corps, and brought all the values they had learned there directly into the army, and how the army embraced them more or less unchanged.
Though long disbanded, this year is the 75th anniversary of the CCC. It wasn't a perfect institution, but I'm a fan at least in part because I recognize in its story all the attributes that benefitted me, (mostly) without the potential for use and abuse, entirely without the lethal content, and oriented toward the production of real, tangible goods that then belonged to the country as a whole ... instead of just bombs, amputations, PTSD, and the shame of a shattered country halfway around the world.