The green nem really does look like a haddoni since it has short tentacles, as well as the folds of the disc on the sand. That said, Fautin/Allen do describe haddoni as having verrucae "light rose to purple" and they also describe gigantea as usually lying "at surface of sand" pedal disc "attached to a buried object. Therefore, your nem could be either. Regardless, while it would be nice to have a definitive answer, it's still a stunning specimen.
I just thought of something. Clownfish don't rely on visual cues (rather by smell) to identify their host. If given the choice between their natural host and another anemone, most clowns prefer their natural host. Since you have two anemones in your tank, and one is definitely a gig, one would assume that if your green anemone was a haddoni, it's more likely that your percs would naturally prefer the gig. But it looks like the green nem is the host, or part host.
When I had two gigs, my Onyx clowns traveled between the two, and though they preferred one over the other, the time spent in the second gig was still significant. Maybe someone with a gig and haddoni in the same tank, along with percs, can chime in. I'm curious to know if the percs spend time in the gig and the haddoni, and how much time is divided between the two.