Here's the result after a bit of tuning. (The temp starts high because I didn't let it cool completely after the previous run).

The ramp rates look good, but the soaks are both about 20s too long. This is caused by my coasting function.

The discontinuity in the cooling was just caused by me taking the glass cover off

It's not perfect, but I think it's good enough at this point. It's certainly plenty accurate for creating prototypes.

In the future I may add an air pump for circulation and cooldown. I also might fuss with the control loop a bit more.

If you're trying to build something similar, you can download the Arduino code here. It won't be plug and play obviously, but you may find it helpful.