After sleeping on it, I believe that extending the white region to cut between the red stripes and the seal will improve the appearance/separation, and make painting easier — select the strips and the offset geometries:
and use Region Builder
Yes
to construct a region of the white stripes and the offset area:
Looking at it again, I believe that it would probably be easier and look better if everything was a monochrome region with differentiation — then the original and partial offset geometries could be used to differentiate to allow painting, then the full-carving would create crisp differentiation between red, blue (painted) and cut wood and initial surface of wood (the seal and surrounding area and the stars).
c.f.,