The gap along the cock side of the gun is zero; the tang sits nicely right up against the wood. However on the opposite side, I can fit an xacto blade's tang in between the wood and the gun's tang, the entire length (from the rear screw hole right up to the backside of the breech).
In terms of my willingness to experiment? I'm very willing. In terms of my skill level? I understand concepts and am usually very handy. But in terms of experience gun building like this? None. This is a first, and the techniques you're describing are brand new to me.
Keep in mind though, this gun is all about the learning experience for me. I'd rather learn "the right way" of fixing issues like this rather than less desirable ways that play down to my current skill set. Now's as good a time as any to start good habits and working on long term proper skills.