You starting this series made me want to get back on my re-plays, so right now, I am playing through Halo 3! This was my first Halo game (so nostalgia bias check), and my mother was not too happy that my father had let me buy it (I cannot remember how old I was, but I think it was below 17 lol). Definitely the pinnacle of the classic Halo gameplay formula, and it manages to craft a mixture of new setpieces and greatest hits without feeling derivative. Plus, the story's ominous and vulnerable Cortana would foreshadow the fascinating story turn for her character in Halo 4 and beyond.
You hit the nail on the head with the music. I think it does lose a little of that synthy charm, but it gains a lot in grandeur and scope. The music as the new Halo ring comes into view is awe-inspiring, and the thundering triumphs of Lord Hood's doomed charge in Voi and the arrival of Forward Unto Dawn stick with me to this day. Plus, I have had acquaintances who considered the Halo 3 "Warthog run" renditions to be the definitive versions, so this may well have been others' first Halo too. Plus, the new use of the piano is wonderful, adding heart to the story's finality that the series never quite had before. There's an intangible, difficult-to-describe melancholy to the score that fits its status as the series finale (for now lol).
(Side note, Princeton's song was a contest winner, per Wikipedia. What that means regarding your assessment I leave to you
Also, the title was apparently "Kill Your Friends," and nixed by Microsoft for obvious reasons lol) Loving this series!