And finally, after a couple of years, I've reimplimented the ticking timer from TalkCoffeeTo.me's Timer in React. I've changed the colors and set the time to 5 minutes, and this is not linked or synced to anyone else viewing this post.
Given the time between implementing this idea originally, the Timer post, and this followup, I had forgotten most of how arcs in svgs work. I rediscovered this stackoverflow answer, which was so useful to pull this apart again. I wonder if this would have been easier to do in Canvas. Another day.