Can I paint cooktop with BBQ paint? Or perhaps enamel paint?

Now that you put it that way.... go to the dollar store and buy a couple cans of oven cleaner. Spray the heck out of them and leave them outside for a day or so. If the stuff dries completely, spray it again. Then hit it with a pressure washer or take them to the car wash if you don't have one. Use the engine clean setting if you go to the wash.

Be careful and watch out for spray back.