Most excellent.
I did some quick googling, and I couldn't find anything specific about rules for translating it to the surcoat, except some mention that the surcoats sometimes had additional charges not in the heraldry.
So yeah, unless we can find better documentation, I'd stick with parti-colored (per-pale, like mine) or quarterly (per cross), and just preserve which colors/metals are in dexter and sinister.
So for me, I should switch the colors, and put the dragon and ankh over their correct colors.