Something based off of L'homme Armee?

I second Chonak's idea, if the plan is to use a hymn.

If you specifically want something more anthem like, would an In Paradisum, say, from Faure's Requiem do the job?

It's often forgotten these days that in the USA, it's Memorial Day that serves as Remembrance Day to honor the memory of members of the armed services who have died, and Veterans Day primarily honors living veterans.

This year, of course, it's the 100th anniversary of the Armistice.

National Anthems Of The Allies
Published 1917

https://imslp.org/wiki/National_Anthems_of_the_Allies_(Various)

The official hymn of the United States Army, "God of Our Fathers", which was composed for the USA's centenary in 1876, may suit your purpose (though it isn't expressly Christian):

https://hymnary.org/text/god_of_our_fathers_whose_almighty_hand

1 God of our fathers, whose almighty hand
Leads forth in beauty all the starry band
Of shining worlds in splendor through the skies,
Our grateful songs before your throne arise.

2 Your love divine has led us in the past,
In this free land by you our lot is cast;
Be our strong ruler, guardian, guide, and stay,
Your word our law, your paths our chosen way.

3 From war's alarms, from deadly pestilence,
Your mighty arm our ever sure defense;
Your true religion in our hearts increase,
Your bounteous goodness nourish us in peace.

4 Refresh your people on their toilsome way.
Lead us from night to never-ending day;
Fill all our lives with heav'n-born love and grace,
Until at last, we meet before your face.

(Text as provided in GIA's Worship III)

I detest the fanfare, but I think the text itself, were it accompanied by a doxology, would be better: here's a fifth verse in the public domain (source info: https://hymnary.org/text/o_come_redeemer_of_mankind_appear):

5. All praise and glory to the Father be,
All praise and glory to His only Son,
All praise and glory, Holy Ghost, to Thee,
Both now, and while eternal ages run.

If one detests the tune itself as bombastic (even sans fanfares), EVENTIDE offers a fit in a different mood.

At the West Point Catholic Chapel, where the sacred and the military often intersect, some of our standard options are "For All the Saints" (with the more militant verses, not the edited version found in many hymnals), "God of Our Fathers," and "Lead On, O King Eternal." The Wilhousky arrangement of "Battle Hymn of the Republic" was also a go-to here for many years, but has mysteriously disappeared from liturgical use since my arrival... we're still singing it tonight for the combined choirs concert, though.

Would I vow to thee, my country on (THAXTED) suit?

Chris Garton-Zavesky,
As several people have posted above, Veteran's Day honors the living, not the fallen. The third verse, which states, "O may thy soldiers, faithful, true, and bold fight as the saints who nobly fought of old and win with them the victor's crown of gold" encourages emulation of the saints by the living rather than any sort of implication that the fallen are all saints... At least, that is how the chaplains and I read it.

The one big concert announced here is combining Vaughn Williams' Dona nobis pacem with the Nelson Mass. For 11/11/11:00 I briefly considered the former's fugue ("Nation shall not lift up a sword" to end) but we're going with Mendelssohn's Verleih uns Frieden. But if I'd discovered it a bit sooner, Obrecht's armistice anthem would have been on the menu instead.

Remembrance rather than Veterans, but here in the UK there is a hymn beloved of Anglicans, called 'The Supreme Sacrifice' which was written to commemorate the dead of the First World War. It rang through my head on October 24 last year when we visited the grave in northern France of a member of my husband's family, killed on that day one hundred years earlier aged just 19. My question is: would it be suitable for use at Mass, or a Remembrance service held just before a Mass? I'm rather doubtful. Words are:

O valiant hearts who to your glory came
Through dust of conflict and through battle flame;
Tranquil you lie, your knightly virtue proved,
Your memory hallowed in the land you loved.

Proudly you gathered, rank on rank, to war
As who had heard God’s message from afar;
All you had hoped for, all you had, you gave,
To save mankind—yourselves you scorned to save.

Splendid you passed, the great surrender made;
Into the light that nevermore shall fade;
Deep your contentment in that blest abode,
Who wait the last clear trumpet call of God.

Long years ago, as earth lay dark and still,
Rose a loud cry upon a lonely hill,
While in the frailty of our human clay,
Christ, our Redeemer, passed the self same way.

Still stands His Cross from that dread hour to this,
Like some bright star above the dark abyss;
Still, through the veil, the Victor’s pitying eyes
Look down to bless our lesser Calvaries.

These were His servants, in His steps they trod,
Following through death the martyred Son of God:
Victor, He rose; victorious too shall rise
They who have drunk His cup of sacrifice.

O risen Lord, O Shepherd of our dead,
Whose cross has bought them and Whose staff has led,
In glorious hope their proud and sorrowing land
Commits her children to Thy gracious hand.