Yes, either Linear or Non-Color data for maps which are not RGB colour maps.
You mentioned you had tried using a cage but that blender told there was an error with it.
When you scale along the normals to inflate it, make sure you do it to the whole model and not to only parts here and there.
Also you mustn’t change anything on the geo except for scaling everything at the same time along the normals (Alt+S), otherwise it won’t be able to be used as a cage.
The parts now where you’re getting black spots seem to be on areas which protrude more than others so the ray distance still doesn’t seem to far enough. Now the problem is if the ray distance is too far from the surface normals, it may start from inside another part of the mesh which means it will hit the inside of the mesh before hits the outside surface of the original surface. This is why using cage is so much better for controlling the ray distance.
The cage can intersect with itself as it is just using the surface to tell the rays where to start from and uses the face normals with the vertex ID numbers to point to the correct part of the low poly mesh (this is why cages have to have the surface normals pointing the same direction and the same vertex order). So if you scale some parts of the cage more than others then that will alter the face normals from the original low poly making it now non-identical to the low poly.
If you’re still getting black parts on the bake after you have a working cage mesh, then I would inspect the model all around and check if the black spots are visible in the high poly.
Perhaps also the black spots that remain may come from parts of the high poly mesh which intersect with itself. I doubt this is an issue here but it’s worth mentioning.