For the legs, leave only the first keyframe and delete all others, so they won't slide.
For the head try to rotate joint for 90 degrees and then bake it.
Found workarounds for some of the issues with rotations, but can't figure out why the head mesh does not move at all, even though it is attached to the same bone as the helmet. https://youtu.be/7BXeSgPZYPE
Started to work on using collision shapes defined in NIF files. Much reduced poly count - not sure if this will translate to actual performance increase.
This took a *long* time. It doesn't help that I don't know what I'm doing, but also Bullet's documentation isn't great - a lot had to be worked out by trial-and-error or reading the source code.
Now the mesh has to be broken into pieces so that they can move with the physics shapes.