Melted pot residue on solid plate cooker
This might not have a happy ending I am afraid. You might need to get a replacement part for the plate.

If it was a true enamel pot (and it sounded like one) rather than an aluminium pot with an anodized surface, that is a metal pot with an enamel coating, once it is heated to above the fusing temperature of the enamel (500C at least, likely much higher), the coating will melt. What you went through is the reverse of the process to apply the enamel. 

Enamels are metal based compounds, ceramic or glass like once re-solidified. It tends to fuse with metal and glass with no defined boundary. Despite that it is typically brittle, it is going to be very difficult to get it off the stove, especially if it is a metal hot plate or a ceramic hob. Enamel is pretty unreactive. Anything that would dissolve it would likely first dissolve your cooker surface. It is also much harder than the cooker materials. Heating it back up to fusing temperature would only help enhance bonding of the enamel to the cooker.

Not a terribly helpful answer I am sorry to say. Hopefully, I am wrong and there is a more helpful suggestion from others.