How are you going to (try to) re-black it, Neil? Having read a good deal around the topic over the years, I have yet to come across anything truly convincing (not tried, just researched) bar abrading the degraded surface layer away - which just sets you up to start over with sulphur leaching and bleaching. That was done to the body of a beautiful Rudall Carte Böhm flute I have, at the almost complete cost of the of its maker marks. It looked stunning in its fresh black shininess, but is starting slowly to dull and turn again - partly because I tend to keep it out ready to play, in shade, but nonetheless… Mind you, I recently acquired/repatriated something rather special in Ebonite from Oz which hasn’t gone off too much - apparently not left/used out in the sun! 
Olive oil rejuvenates the material I have found, I’m not after black and will be happy with my green/brown colour, problem being unless handled often it doesn’t move really. When It’s done and keys back on, I’ll ask you to post again if there’s interest, after all these are those infernal band flutes. LoL
I have several Hawkes & Son instruments made of ebonite. The condition of the ebonite on these instruments varies from glossy near jet-black to dull mottled brown/green. There are measures that can be taken to slow degradation, but, as Jem states above, I’ve not seen a convincing restoration of a badly damaged finish. Two of the flutes received new pads, and while the keys were off, I had the flute lightly buffed, so as not to damage the maker’s marks, and coated with a hard wax. This treatment restored the surface gloss, and darkened the color of the instrument from a mottled green brown to a more consistent dark olive. To maintain the finish, I try to keep the instrument(s) in cool, dark, dry conditions and minimize exposure to oxygen. So, no leaving them in the sun or under hot artificial lighting. Store inside a case with a case cover. Thoroughly dry after use. After drying the flutes and before placing them in the case, I’ll place a couple of drops of mineral oil on a lint free cloth and give them wipe down, which provides light film of oil on the surface to keep them glossy and reduce exposure to oxygen. Occasionally I’ll place a small packet of desiccant in the case during humid summer months. I play the instruments daily, and this has kept the finish reasonably stable for several years, though there is some light discoloration around the tone holes and embouchure.