My current plan is to build a small fire inside the forge using just some kindling, and let that burn out. When that's cooled a bit, I'll start a second woodfire using logs, and let that burn for a while. A simple wood fire with no forced air isn't going to vitrify the clay, so this is an exercise in driving off water. Again, I can't find much in the way of advice on how to dry thick hunks of clay, so I'm flying blind.
Yes, it's on fire, but you can't really see it because the sun was quite bright that day.
Burn 1 went to completion without a hitch: no spalling of the clay at all, and a nice hard surface resulted on the inside. Round two, with the bigger logs, begins.
This also went well, although it took a lot longer than I'd hoped. To keep the fire "in" the forge, I had to keep chopping away at the lower parts of the wood to get them out of the way so the fresh (burning) wood was below the top.
As you can see, the second firing went well. There was either a little spalling, or there wasn't any, and I just cleaved off some loose ash/clay when cleaning the coals, but either way, there are no cracks or major cleaves, so I'm ready to move on to the High Firing!