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Like the other rider said, windex and a microfiber cloth will clean it up. All you have to do is blend at the edges. That denim paint wears to a shinier finish when rubbed, so be careful. I am guessing the shiny areas surrounding the old badge outline are from where a cloth or any other material was channeled around the badge when drying or cleaning the bike. A lot of guys get shiny patches where their legs rub or seat bumpers sit as well. Denim will not keep a uniform finish unless it is not touched at all.
I would think that it wouldn't have to be perfect if you are placing your new tank badges more or less directly over the space where the old ones came off ....
I'd just get it to look as good as you can ... minimize the effect to the extent possible and then put the new badges on ... before long, the 'wear pattern' will begin to match the new badges and it will look natural ....