Your choice of image of Neferkare Khendu's cartouche from the king list proves my point that it is probable that the horizontal lines were painted on ... otherwise, where are the lateral carvings on the 'ch' glyph while we know there should be none on the 'Ra' glyph positioned first in the cartouche.
I know what you will argue .. the Ra glyph is positioned first on Raufu's cartouche, too.
If that's the case, why isn't the 'ch' glyph carved on your illustrative example?
Stalemate, I'd say.
SC: Well, to be fair, the paint discussion was with Origyptian. My point was to demonstrate that the kh sieve is drawn smaller than the Ra disc. The Khufu disc is given the same proportions as the Ra discs of Radjedef, Rachaf, Menkau-Re etc. The AE would not dishonour the Ra deity by giving the sieve equal size proportion than the obvious Ra discs (that have also been given honorific transposition).