I think given the current feature set it’s intractable. The stretch-to constraint helps a lot in some cases, but either I’m applying it wrong, or it’s still not perfect. Morph Targets (aka blend shapes? aka joint-controlled-RVKs) pretty much fix all problems, albeit moving the problem into the artistic realm and out of the mechanical realm.
If you download my latest blends, you’ll notice I’ve put two armatures, one on layer3, and another on layer4. The layer3 armature is very simple, and corresponds to major bones. The layer4 armature is extremely complex, with many bones in places for non-bone constructs like muscles, ligaments, and for shaping the figure.
I plan to use the simple armature for posing, and the complex armature will have constraints to the simple one. Then I’ll remove all nonessential bones from the complex armature to see if that will help deformations of the model.
This is going to be a long project, so I will probably not do it until a long weekend. 
I know it’s probably hard to quantify, but any more hints you could give me about why their faces don’t look real would be great.
Any chance it’s the nose (especially, places where the nose fits to the face)?
Excellent critique. Something was bothering me about the image. I think that your suggestions nail it. You and osxrules both noticed the curvature of the models’ backs don’t fit well inside the circle. That’s actually a shortcoming of the rigging of the character. If I bend their backs more, their front sides begin to deform very badly.
Yes, that’s actually one of the happy accidents I felt about that image. They look like they’re dancing in a circle, until you look at their feet, and they’re in a standing pose. It makes me laugh every time I look at it.
It might be considered jolting or otherwise bad by most artists, though. 
I keep adding and deleting vertexes. It is my first 3D project ever, so it doesn’t seem odd that I should keep realising I’ve totally done it wrong, but it is what it is.
I’ve found the vertex groups to be a difficult enough interface that I’m trying to avoid it until the vertexes are set in stone. For now I keep letting the computer decide vertex weights based on closest bones.
Once I do seriously weight the vertexes, that mirror script will likely come in quite handy.
It is true. I downloaded the script and played with it for some hours. Inside the .blend they provide, I’m able to do some interesting hair effects, but I’m totally unable to port the script into my own .blend. I guess I need to port my mesh, armatures, etc into the fibre .blend? I resist doing that because my .blend has so much of my workflow built into it now, with windows precisely sized and laid out. 
Sorry. I was genuinely interested in what was the ratio in this case. But yeh, sometimes by showing interest in something you draw attention to it. I’ll try to just let it be what it is and stay away from the politics. I don’t have much energy or tolerance for politics anyway. Thanks for your input. You seem as exasperated about this as I am, and yours is a good way to solve the problem.