NPEAs
My first comments revolve around the SS domination of the NPEA Schools. This did NOT happen until the 1942-43 period.
Next, the NPEA Schools originated from the Prussian Ministry of Education. Rust, through Haupt, formed the schools as a higher education boarding school as a Present for Hitler in 1933. Haupt was an educator working in the ministry at that time who also was involved in the HJ movement and was Hitler's first choice for HJ top post, but he declined the post to remain in education.
Next, Heissmeier the SS Administrator for the schools after Haupt left the ministry was also a member of the Ministry of Education under Rust (Prussian Ministry of Education head in 1933 and appointed the Reich Minister of Education in 1934). So while an SS member and General, Heissmeier was an educator first and an assistant to Rust until midwar when he became head of the schools after the SS assumed control.
Heissmeier had been the head of the schools for the Reich Education Ministry under Rust from the time Haupt left until the end of the war.
Next, my feelings on the triangle in question is unsure. While possible, I find it hard to believe in anything unofficial being worn. The only possible reason is the triangle MIGHT be from the mid 1930s before the standardization of the NPEA triangles in 1938-1939 period. Doubt will always remain until a period photo can be produced IMO. AFter the war began, the triangles were phased out the the SS sleeve eagle was worn after the control of the schools reverted to the SS in 42-43.