I got the override layer to work. The issue was that I set the weight of the base layer to 0, because I thought you need to blend between the two. Actually, you only need to blend in the override.
However, I noticed that the override layer doesn’t overwrite animation sequences. It seems to be additive in relation to them… which defeats the point of it being an override. Is there a way around that, short of baking to the control rig?