Mysterious offset when alter armature's edit bones?

As Serge L suggested it was possible to achieve the expected result by first removing the parent/child relationships from each object, then modifying the edit_bones to match the template skeleton, followed by finally re-creating the parent/child relationships for those objects.

Here is some code that finally got things working for me:

import bpy
from mathutils import Matrix

def get_bone_children(parent, objects): 
    children = [] 
    for ob in objects: 
        if ob.parent_bone == parent.name: 
            print(bpy.data.objects[ob.name])
            children.append(bpy.data.objects[ob.name]) 
    return children 

def clear_parent(child): #clear parent keep transform - https://blenderartists.org/t/preserving-child-transform-after-removing-parent/616845/3
    # Save the transform matrix before de-parenting
    matrixcopy = child.matrix_world.copy()    
    # Clear the parent
    child.parent = None        
    child.parent_bone = ''
    # Restore childs location / rotation / scale
    child.matrix_world = matrixcopy

armature = bpy.data.objects['Armature']
bones = bpy.data.armatures['Armature.001'].bones #the template bones

bpy.ops.object.select_all(action='DESELECT')
bpy.context.scene.objects.active = armature
bpy.ops.object.mode_set(mode='POSE') #must do this or else context will not be correct
for pb in armature.pose.bones: #Reset Rotation , Translation and Scale of bones through Script - https://blender.stackexchange.com/a/147342/32655
    pb.matrix_basis = Matrix() #  == Matrix.Identity(4)
bpy.ops.object.mode_set(mode='OBJECT')

childObjects = [] #stores all bones in this armature
for i, bone in enumerate(bones):
    children = [] #all of the children connected to this bone
    for c in get_bone_children(armature.data.bones[bone.name], bpy.data.objects): #Parent object to a bone and object becomes offsets - https://blender.stackexchange.com/a/139180/32655
        children.append(c)
        clear_parent(c)         
    childObjects.append([bone, children])

for i, bone in enumerate(bones):
    #match the head/tail local positions between the two armatures
    head_pos = bone.head_local 
    tail_pos = bone.tail_local 

    armature.data.bones[bone.name].head_local = head_pos
    armature.data.bones[bone.name].tail_local = tail_pos #Removed from main loop because makehuman rigs showed overlapping bones, besides the tail is unnecessary for pose

    #These lines are critical!!
    bpy.ops.object.mode_set(mode='EDIT') #must do this or else the new positions will not be updated
    bpy.ops.object.mode_set(mode='OBJECT')

#restore parent relationships
for i, childObject in enumerate(childObjects):
    bone = childObject[0]
    children = childObject[1]
    for c in children:  

        matrixcopy = c.matrix_world.copy()    

        c.parent = armature
        c.parent_bone = bone.name
        c.parent_type = 'BONE'

        c.matrix_world = matrixcopy