There has been recent development done with blenders gltf exporter, so try exporting with a current development build of blender, you can get a daily build or go to GraphicAll if you don't want to compile yourself.
Using a recent build (week old) I can export your blend file to gltf and do not see the issue when importing back into blender, which I do see when importing your sample glb file. Using sandbox.babylon.js also shows the new export to work.
Another thing to try is to apply the transformations to the armature and mesh, the two in your blend file do not have the same location. When the two are moved separately you can see a similar distortion, try it by moving the mesh object in blender separate to the armature.