This is why I was hoping to find a rigging partner for my models in the first place.  It doesn't get much dumber than this when it comes to getting a finger to move properly.  On my screen, those spherical influence zones are always right at 0,0,0.  I don't know if they're supposed to be there, but it would make more sense to have them with the bone.

I even adjusted the red sphere down just slightly.  Instead of those knuckle areas working properly, the finger started bending at the wrong place, and distorting badly with anything more than a slight bend.

So, sadly, this is taking me away from the modeling that I need to be doing.  If anyone still wants to rig my models and share 25% of the sales profits here on Rendero, let me know.  I'm still interested in doing that, but again, rigging these myself is becoming too time consuming.

Thanks to everyone for all  your help!