Have you tried Animation Rigging (Rig Builder on) with Apply Root Motion on? Please let me know if it works for you. On my case, animation that applied root motion will be broken if I leave Rig Builder on.
I have no idea about the base code of Animation Rigging and Animator Root Motion, and I just tried many times trying to figure out how to use Animation Rigging with Animator Root Motion.
So, my conclusion is: it looks almost impossible to use Animation Rigging (two bone constraint) with Animator Apply Root Motion. For my experience, if you leave the Rig Builder on, Apply Root Motion and start an animation, your current and next, next next, next next next animations are all broken.
