Nissan didn't just stick stuff any old stuff on cars just to "get rid" of it, despite any old wives tales you may have heard.....
Not all S130s were 'ZXs'. The Japanese home market S130 variants that were fitted with the L28 engine were known as 'Fairlady 280Zs' ( more specifically 'Fairlady 280Z-L', 'Fairlady 280Z-T', 'Fairlady 280Z-L 2by2' and 'Fairlady 280Z-T 2by2' ) so your 2-seater car could easily be a Fairlady 280Z-L or Fairlady 280Z-T.
Whether the emblems / decals you describe were originally on the car when it left the factory is another question.....