I know you're being sarcastic, but I would reply that it probably doesn't matter as much as you might think. The wood can only affect the vibration of the strings to the extent that they are coupled, and they are only coupled in two places: at the nut, and the bridge. I would further say that, although I can't really prove it, I strongly suspect that it is the part of the wood closest to these coupling points that most strongly contributes to the tone, i.e., if you changed the neck wood, it would affect the tone much more than, say, changing the type of wood used for the body wings in a neck-through.
The point at the neck is not at all disturbed relative to an ordinary Jem, and the point at the bridge, I would argue, is not disturbed very much since even in a normal Jem, it is to some extent isolated from any vibratory influence from the body by way of the floating bridge.
Pure speculation on my part, however.