I have it working! Thanks to theConcurrentHandsControllersExamples.scene
See screenshot. Now it aligns and also no(!) lag. Same as in the meta "main menu".
The (last) setting I had to modify was on the OVRManager.cs. "Controller Driven Hand Poses Type" needs to be "Conforming to controller". See screenshot attached.
I can only attach one screenshot, so I will add another reply with the result.