Hi Jason,
A good work. These "mushroom burners" have a great advantage over the wick burners. They produce greater heat under the boiler due to the wider burning area. Thus, the steam generation happens faster and more intense. Another advantage is that the gasification of the methyl alcohol in the mushroom head and subsequent combustion produces less soot, which then settles under the boiler.
I have never experimented with making my own wicks. There are quite inexpensive cotton wicks that are infused with fiberglass. These wicks hardly carbonize at the tip and again reduce soot formation. This is true for the simple wick burners.
Burning the wicks in the mushroom head burners must not happen anyway, since the wicks only serve to transport the alcohol into the heads, where the alcohol mixes with air (gasification).