Use Nudge..... that lets you move the tracks a tiny bit at a time. You can also zoom in and move them manually then use nudge to get them perfect.
Since they do sound like the out of sync remains constant that's the path I would use.
On occasion, I need to realign a track I have moved and zoom/nudge works perfectly.
Just curious, what is your equipment and soundcard etc? Normally, things recorded in sync tend to stay that way. Since yours didn't..... makes me wonder about the gear, card, drivers, etc.....
Cool song BTW