Cover the badge with aluminium foil. You can use baking foil for this, although it is very thin and you will have to be careful when doing the rubbing down part. The best foil to use is the thicker foil that take-out food dishes are made from. You don't want it too thick, because then you can't get the detail you need.
However if you are careful even thin foil will give you an excellent result that will be as tough and as robust as any when finished.