I had a similiar Problem with a Quadruped, where Parts of the Animation were completely broken: the Head had a wrong position while the ears were in the right position.
Apparently the Parent Child structure of the Deformation Bones is not suited for baking and does not always work correctly outside of Blender.
I solved this with the ORG Bones (Bottom Last ...
That is odd. It looks like the Rigify rig is set to IK. You have to select one of the bones for the arms in pose mode and set the IK-FK (hand.L) value to 1.00. See picture
You can adjust this for every limb and is one of the useful options of Rigify.Hope this helps!
I found out that rig_id is pretty finicky with the names you might try changing some things about the name and rerun the script to see if that fixes your problem.
On Blender 2.79, having the word "rig" anywhere in the ID name would cause the script to fail (no N menu) without warning.
That is not the case in Blender 2.81 however: if you put a Capital letter ...