Having revisited this thread now several years later, I think I understand the charcoal fuel problem better. And possible solutions.

I think I missed the point that though charcoal may be hotter burning, it is also much less dense than coke. So to melt the same amount of iron (with the same amount of heat -- regardless of burn temperature) I would have needed the same
weight of charcoal per unit weight of iron. And the burning zone would have needed to be proportionately larger to produce the same amount of local heat.
There are two ways to increase the amount of charcoal available to the burning zone -- increase the diameter of the cupola, or increase the height.
Increasing the diameter would increase fuel mass as the square of the dimensional increase. Increasing the height would increase the mass of fuel linearly.
Since the burn time was so short, more height would help with that. A sawed-off cupola isn't ideal for much burn time. Even with the short extension, it wasn't adequate, although better.
Increasing the diameter would increase the temperature of the hot area. And this would have possibly been a benefit in melting sufficient metal to fill the well and keep it hot. It's also more efficient with less proportionate heat loss to insulation.
The proportion of charcoal to metal in a charge would probably needed to be higher than with coke (even by weight).
As the metal charge and fuel drops down the cupola barrel, it basically determines metal feed rate to the molten puddle. With a fast burning fuel like charcoal, that metal feed rate is faster as well, since the iron is dropping into the heat zone faster, coming along for the ride with the charcoal.
So, in general, I'm going to say, a specifically designed charcoal cupola might better be taller even than a conventional coke cupola, and the fuel to metal ratio would likely need to be higher. Blast will likely need to be be lower since the charcoal is less dense, and the weight of oxygen needed is proportionate to the weight consumed of a less dense fuel.
Anyway, I think I can see what might have needed changing.
