Answer
Resolve the Responsible identifier into an actual system User ID by calling Person_Info_API.Get_User_Id against the Responsible/Responsible ID attribute value, rather than a name-lookup method — this returns the genuine User ID a Streams notification can actually be addressed to. This only works correctly if the underlying Responsible attribute genuinely stores a person/responsible identifier value that Get_User_Id can resolve; if that specific object's Responsible field stores something else, the same general technique, finding the right API method to convert whatever identifier the field stores into a genuine User ID, still applies, just via a different specific API call.