Over the week I made another mug. Much better formed. I fired it today and the results are quite pretty. Unfortunately I had very little charcoal left and I couldn't fire it for more than about 45 minutes, which is nowhere near long enough. It's since broken :( Also, not nearly enough glazing. Lessons have been learned, however!
One of those lessons is to buy a better quality thermocouple that won't melt 350 °C below its rated temperature.