You can not believe CIO-S has returned SW2 application saying your application does not fit to SW1 !!!!!??? They thought or considered AEO based application as SW1 and said your job is not in list of 29 professions. By the way yoou clearly mention on your envelope that it is SW1 or SW2. Anyway, it happens. And I do not understand why poor applicants should bear their mistake consequence.
Make sure you include a clear cover letter. And do not send any document assuming they will understand. They do not understand without clarification in even simple cases (, like work timing in a week) and you assume you are dealing with robots. Either black or white and no grey