First of all, hilarious intro. Second, why should you pick a sad version for a victory theme? Wouldn't a powerful, dramatic version or the original be better suited?

sad because it's a bittersweet victory, thousands of NCR men lay dead, the only one of two factions in the wasteland that represents democracy. They may have been the enemy, but they were still americans clinging to the ideals of old america

Also it could represent the death of Democracy in America if you decide to go down the path of Martial Law and Expanding Presidential Powers. Only when you Reform the USA should you get a Patriotic Anthem and if you create a New American State you get a twisted and wrong version on the National Anthem aka. this one

https://youtu.be/UiWTIzO-NR0

https://youtu.be/jLrICGrx5OI

This one could work too. It has that lingering sense of regret. And much like Stillman, the Reformers have to confront their own sins and try to make things better.

https://youtu.be/5TXVU7RqH-o

And this one when you go down the Enclave Reborn path. First a triumphant blare, then some haunting, ethereal droning... signifying the terrible realization after.

Edit: When you go down the Nation Reborn path, the Star Spangled Banner fits perfectly. I would not change that.