Part NCO has been suggested, but has insruction really been designated as non-commercial?
Yes, See the Comment Response Document (CRD) to NPA 2009-02b:
30. As regards the applicable operational requirements for approved training organisations, it is proposed that flying training by ATOs is conducted in accordance with either Part-NCC or Part-NCO, depending on whether the aircraft is complex motor-powered or not and regardless of whether it is a commercial or non-commercial activity (Article 1(2) point 9). This approach should be in conformance with the present situation in Member States where training schools are most of the time required to follow the national general aviation rules.
The proposal was later ratified by the EC and was included as Article 5(5) of the amended Regulation 965/2012.