That was Beautiful
Indeed, a very good summary though I'd like to add something imho important to the end. ^^
[Boromir:]"Farewell, Aragorn! Go to Minas Tirith and save my people! I have failed."
"No!" said Aragorn, taking his hand and kissing his brow. "You have conquered. Few have gained such a victory. Be at peace! Minas Tirith shall not fall!"
Boromir smiled.
- The Two Towers, Book Three, Chapter One: The Departure of Boromir -
It is not just a simple promise from Aragorn, not just soothing words for the dying Boromir. It is the testimony of Boromirs Salvation.
You have conquered. Aragorn is not talking about the fight, the twenty dead orcs lying around. Boromir has conquered his lust for the Ring, broke free of its influence. He was about to take the Ring from Frodo, possibly killing him in the process, whom Boromir has sworn to protect. But at the brink of it he turned away.
Few have gained such a victory. Isildur himself was not able to do the same, turning away from the Ring, and he was counseled by Elrond and Cirdan. But Boromir did. And in his turning away he achieved redemption, victory, by doing the ultimate good action: Sacrificing himself to protect his friends.
Boromir dies smiling, not only because of the promise that Minas Tirith shall not fall, but also because of the assurance that his sins are atoned for.
I agree about everything you wrote.
As you said, at the end, Boromir won that inner battle. Battle between his character and ring's corrupted power. He wasn't wise leader of his people, I must say that. He felt into trap by ring (although he had the best intentions for his people), and at the final moment of that battle, when he was maybe in doubt to kill Frodo, his great side of character prevailed. His honor and glorious side prevailed against corruptive nature of the ring. Simply that was value of character which never could be corrupted. That is great strength of Boromir. And as you said he achieved redemption with his last act, when he tried to save little ones.

Boromir was reincarnation of the last king of Gondor (House of Anárion), Eärnur in some way (sadly we haven't more info about Eärnur).
Reincarnation in character properties, physical abilities and leadership. Both of them was great warriors (last great members of their houses), leaders in battle but sadly not wise leaders. That lack of wisdom, costed them their lives.
P.S. Concerning inspiration of making those characters, I have read "TOLKIEN'S RING" by David Day. It is really good book in term of analysis of Tolkien works with other myths and legends and real history facts of this world. There is nice analysis and it is presumed that Tolkien used character of Roland, the chief paladin of the emperor Charlemagne, as base material for Boromir's character. So I recommend you to check it if you haven't known this already, it is pretty interesting material.

Regards,
CragLord