Some of the detail might be too fine for even a 1/16" bit. To make these go at a reasonable clip, I'd select v-carve, set the flat depth to like .080" or so, using a .020" 30 degree engraving bit for your v-bit (you can set this up in VCarve Pro) and use a .125" bit as a flat area clearance tool. Then like Gerry said, you can spay your finish first, then engrave, sand, paint fill and re-spray.

Realistically, this job might be easier and faster done on a cnc laser (hehehe)...

For the sealer (pre-cutting) coat, I'd be more inclined to use shellac if possible; it dries a lot faster, not as harmful as lacquer, and you can spray poly over shellac. It will also build up faster than lacquer, which you'll need to fill the pores on the wood where lacquer would just "float" over the surface.