Does anyone know of a reliable source for the story about how the Maskilim made a play to mock what a milchama would look like according to the torah/chazal, in which they depicted only the Chofetz Chaim and Rav Chaim Ozer left standing to go to war after all the ovrei aveira were sent home? It is said that when Rav Boruch Ber was told about this he responded that they failed to see the end of the story where the 2 tzadikkim were miraculously victorious because of their great merit.
This is not really a good answer as this isn't an actual non "story" source (as requested by the question), but I'm putting this down as the text below seems to be shared in a number of places, mentions the Yiddish Theater as the source and the cast of characters is slightly different (VG+SA instead of CC+CO). If anyone comes up with a better source, I'll delete this.
The Yiddish Theater was not known for its championing of Torah values and so it was not surprising when two students came running to the Brisker Rav, breathless with indignation:
Does the Rav know about the new play the Yiddish theater has put on? The people associated with it should all be put in cherem (excommunication)! They've made a satire on the Torah!
First, one of the actors says "Who is the man who has built a new house and not inaugurated it? Let him go and return to his house lest he die in the war and another man will inaugurate it". So, ten people get up and walk off the stage.
Then he says "And who is the man who has planted a vineyard and not redeemed it? Let him go home lest he die and another man redeem it". So, another ten people get up and leave the stage.
Then he says "And who is the man who has betrothed a woman and not married her? Let him go home lest he die in the war and another man marry her". So, another twenty people get up and walk off the stage.
And then he says "Whoever is afraid, let him go home so he won't scare everyone else". So now everyone leaves the stage except two actors who play the Vilna Gaon and the Shaagas Aryeh.
The Vilna Gaon says to the Shaagas Aryeh "Kvod HaRav you take the first shot", and the Shaagas Aryeh replies "No, no, I insist after you".
As they argue about whos going to start the war, the curtain falls and the audience laughs and claps. Its terrible!
The Brisker Rav paused and then said: "Well, whats wrong with that?"
The jaws of the students dropped. They gazed at their Rav dumb-struck.
The Brisker Rav continued, "The only thing they forgot is the last scene."
"What last scene?"
"The last scene is where the Vilna Gaon, and the Shaagas Aryeh win the war. "
This story is brought in the biography of R' Baruch Ber (pg. 130-131) by Rabbi Yitzchak Edelstein whose father was a student of R' Baruch Ber. He himself knew R' Baruch Ber when he was young and also attended his funeral, which took place during the Holocaust. As he puts it:
סיפר: בבריסק, בימי כהונתו של הגרח"ס, קיים חוג מסויים הצגת חוכא וטלולא על הנושא "צבא עברי". לפני צאת הצבא למחלמה הכריז המפקד: "מי האיש אשר בנה בית חדש ולא חנכו, ילך וישוב לביתו, פן ימות במלחמה ואיש אחר יחנכו." מיד קמו אלף חיילים, הצדיעו ועזבו את המערכה. קם מפקד שני והודיע: "ומי האיש אשר נטע כרם ולא חללו ילך וישוב לביתו פן ימות במלחמה ואיש אחר יחללנו." הלכו להם כעוד אלפיים איש. התמתח מפקד שלישי וקרא: "וומי האיש אשר ארש אשה ולא לקחה ילך וישוב לביתו פן ימות במלחמה ואיש אחר יקחנה." התרוממו עוד אלפיים איש ובשתיקת אלם עזבו את מקום ריכוזם. בא מפקד רביעי והכריז: "מי האיש הירא ורך הלבב ילך וישוב לביתו ולא ימס את לבב אחיו כלבבו." הצדיעו עוד שלשת אלפים חיילים והלכו להם. על הבמה נשארו רק שניים, והם: הגאון מווילנה ובעל "שאגת אריה". התחילו שניהם במשא ומתן של הלכה, מי קודם למי במצוה זו של מלחמה באויב. כשסיפרו להגרח"ס על דבר ההצגה וסיומה, אמר: "השחקנים צודקים, אלא שיש להוסיף, כי דווקא שני הזקנים האלה ניצחו במלחמה."
"He [R' Baruch Ber] told over: "In Brisk, during the reign of the GRaCha"S (the Gaon Rabbi Chaim Soloveitchik), a certain group organized a satire play on the subject of "a Hebrew army". Before the army set out to war, the commander announced: ""“Is there anyone who has built a new house but has not dedicated it? Let him go back to his home, lest he die in battle and another dedicate it." Immediately, a thousand soldiers rose up, saluted and left the battlefield. The second commander stood up and announced: "Is there anyone who has planted a vineyard but has never harvested it? Let him go back to his home, lest he die in battle and another harvest it." And so, some two-thousand more men left. The third commander rose up and called: "Is there anyone who has paid the bride-price for a wife, but who has not yet married her? Let him go back to his home, lest he die in battle and another marry her." Another two-thousand men rose and in utter silence left the gathering place. Came the fourth commander and said: "Is there anyone afraid and disheartened? Let him go back to his home, lest the courage of his comrades flag like his." Three thousand more men saluted and left. On the stage remained only two, and they are: The Gaon of Vilna and the "Sha'agat Aryeh". The two began a back-and-forth in halacha over who has precedent in this mitzvah of battling an enemy.
When they told the GRaCha"S about this play and how it ended, he said: "The actors are correct, however it must be added, that precisely these two old men won the war."
The story is also brought by Chaim Walder here. He quotes it out of one of Rabbi Shimon Meller's books about the Brisk dynasty but doesn't specify which one. In his version, the group who set up the play were maskilim. I haven't managed to get access to Rabbi Meller's books.
Unfortunately, I have yet to find external evidence for this play. It's possible that it first appeared as a satirical story in one of the haskalic publications of the era and was then made into a play. The style described is very in-line with what the more extreme maskilim would do, which is satirically mocking Torah. Perhaps it was just a one-time thing, though (from what I've read, plays that were preserved were usually performed multiple times).