If you really want to get it fixed right....and I mean a great job done.....go to a custom motorcycle shop, or a good metal fabricator that builds/fixes custom motorcycle tanks. I have seen these guys do tank repairs by tig welding and not mess up the rest of the paint job or warp the metal. They usually know someone that can do a great job of spot painting the area and you won't be able to tell. Remember, most custom bikes have custom paint jobs on the tanks and no one wants to have them completely redone when they ding a tank with a gas nozzle or something else. Plenty of vids on YouTube of this repair process.
I still think that if you lower the emblem just enough for the emblem to cover the hole, that it won't be super obvious to most people.