How to reflect individual bone axis? I don't want to change the bone roll, that doesn't accomplish anything.

When I have a bone, I want the Y and Z axis to stay the same, but I want the X axis to reflect across the local Y axis. If I try and change the bone roll, it always changes both the Z and X at the same time, even though all I want to do is flip the X axis of the bone in edit mode. "Switch Direction" almost accomplishes this, except then it reverse the head and tail location.
I haven't got a full picture of what you want to accomplish with this but:

What you can do is to have an armature that is scaled to -1 on one axis. That will give you an inverted coordinate system inside that. You could then drive bones on the deforming armature with those bones.

AFAIK bones will end up as matrices that deforms the mesh. Having a negatively  scaled matrix on one bone will also scale the deformation accordingly. By using a controlling bone that exist in another coordinate system, this problem will be limited to a non deforming armature, and this is fine.