Some of the chorded-note buzzing decreased a bit when I leaned forward. Some of the rattle's still there though.
None of the hardware is loose. That's one of the first things I checked.
I think the reality is that I just got one with a week neck. Bad luck of the draw. I may still pursue the warranty option... worth an ask I think.
What I'll most likely end up doing is just add a great deal of relief until it's basically set up to fender specs (about .012 to .014). Hopefully I can get the action low enough to where I'm comfortable. A lighter touch will probably side step the A string rattle, but the chorded notes don't seem to be effected by a light touch. I may replace the bridge with a hipshot, if I feel motivated to do so. It'll at least give me more adjustment options. We'll see.
If all that doesn't work out, I'll get the frets leveled. That should help make the bass playable. Down the line, when it's time to refret, I can have the fretboard either re-leveled or, if I want to get extreme, get a luthier who knows what they're doing replace the board entirely.
Ultimately, I think I'll just have to get over it. Yes, I paid too much for me to feel good about a new bass that has such an extreme issue, but it'll still make sounds. That's what it's there fore after all.