Regarding the interior of the wood not being soaked by the stuff when it was cut open. (35:32) I suspect moisture content of the wood is a factor. A similar challenge is faced when cooking French toast, with particularly thick slices of bread. When making French toast, you want the custard to fully soak the bread, but a similar effect occurs if you use moist bread, where the middle is not soaked as well as the outside, it looks almost exactly like that cross section of the wood in the video. The solution is to leave the sliced bread out overnight, to allow the moisture that is filling all the capillary fibers to dry out. Then you can make perfect French toast because the dry capillary fibers are much better at sucking the custard in to the center, like a bazillion little straws.

Thus, I suspect drying the wood ahead of time would help?

P.S.: on the thickly sliced French toast, to get it cooked evenly inside with a nice exterior crust, after custard saturation (don't overdo it) I recommend searing the slices quickly in a pan with butter, then throwing in an oven at 350degF for 3-4 minutes. My custard recipe per serving is approximately 1 cup dairy, 1 egg, 1 tablespoon of honey, and a little pinch of salt. Briefly zap the honey in microwave to make it easier to mix.