Loading gltf animations from separate file

Here’s the setup: I have a GLTF file with a character and some animations. I load the file, add the skin to the armature, clone the armature, add it to the scene, animate it - everything looks fine.

Now, as an experiment, I clone the GLTF file - so I have two identical copies of the same file. I load the armature + animations from the first file, and the skin from the second file. I do the same steps as before - add the skin as a child of the armature, clone the armature, etc - but now the character looks like a crumpled up piece of paper. None of the animations are correct.

The reason for doing this is that (eventually) I want to put the animations and the armature in a file by themselves - I have lots of skins that use the same armature.

I thought that I had solved this previously - even went back and looked at some of my old postings - but apparently not. Or perhaps something changed with Blender 3.