How do I reference a publication in my CV where I am alphabetically listed as an author but the citation lists the organization?
You should definitely keep the original reference format but could easily add a simple footnote/inline note to elaborate your involvement. I would do something along the lines of:


  [P7] Organisation name**. Awesome paper written in large writing group. Published in the Journal of Awesome Research [3.14], pp.200-222. 2017
  
  ** Note: Published under organisation name, I am listed as nth author and contributed x.