FWIW, and I am probably late in helping, but it may help in the future.
I would take a torch and burn the rest of the surface on the inside, and lightly sand it. This way it would appear to be the way you wanted it to be, if anyone were to check it out. Because the entire area would have the Custom Burnt wood look...hit with some clear coat, and it is a real one of a kind peice.

I think it would look better than paint, you said you are already too thin to really sand it out.