I've done up a rough prototype housing 3D printed with PLA to confirm my dimensions were good and for easier testing.

It printed a bit wonky on the bottom but good enough.

I did another test with the hot mug and was able to yield 260mV at peak. I still have not applied the thermal paste between the surfaces of the thermoelectric generator. I ran the fan from a separate 5V source to see the effect on produced voltage. I was able to get up to 290mV peak thanks to the extra temperature differential.