Your mapping for the segmentMembership_status looks fine to me, but I don't think you need the \\ escaping the periods on the first name and contactID mappings. Those are only needed if you're referencing an identity namespace with a period in the string. It looks like those are just standard XDM paths. That should fix those.
Can you share which connection spec ID you used to create your output schema? I'm guessing the segmentMembership_status has something to do with the output schema that was created.
Something else you can do too is create this mapping in the UI, then use the API afterwards to pull out the created mapping set. That way you have a known working payload to use a comparison to see what's different from your request.