The hydrogen peroxide definitely worked, no more brown jelly and it has completely recovered. I got the idea to dip h2o2 from another thread, where someone was fighting BJD on a duncan colony... I will try to find and link it. When your elegance looked like mine, was there brown jelly and slime? My elegance was in the tank for 2 years with no issues, wondering if it took the h202 dips so well because it was very healthy(before the infection). My only concern about dipping a new coral would be further stressing it out, potentially to the point of death... However, if it has an infection, you have to do what you have to do. Could you post pics of it later and give me info about your tank, maybe I can help you out.
Edit: It is difficult to see where the coral has the infection because elegance love to close up when stressed. However, when turkey bastering it, some of the flesh would fold back, and I noticed a finger nail sized hole down to the skeleton inside the coral, near the elegance's mouth. I assumed this is where the infection started, and as no more brown jelly appeared, the coral started to secrete a dense white string almost (almost looked like the stingers lobos have when attacking a near by coral). Anyway, it started to cover the 'hole,' I assumed it was a scab of sorts and did not attempt to remove this white.