I've never owned a bike with that routing, but I worked on and test-rode many when I was a bike mechanic. Generally, I would route cable in the most "natural" path, which was usually on front of the bars. New bikes often came with long,clear flexible covers to go over the cables and smooth the feel. I haven't seen those aftermarket.
One suggestion in setting them up; run cables and adjust brakes before securing cables to bars or taping bars. Forcefully apply brakes to fully seat cables and ferrules into where they belong. THEN adhesive tape cables to bars and handlebar tape over it. Remember you might need to stretch the tape little since the effective diameter of the bars is now bigger.. most tape barely gives you enough already!