I'd actually want a 0.5" gap between the center section of the bar and the end of the leather wrap. Use that bit of naked bar for computer mount, light, bell, what have you.
Not me, not on that bike, it's too clean and racy looking.
I've seen (and own) some bars with shorter lowers than that, so I think you *could* lop off a half inch and still have very usable bars. I personally wouldn't do it but I like a really long flat down low whenever I can get it; to the point where randonneuse style bars are my favorites.
Lovely bicycle, BTW. And it would look really cool with the stitch-ons. I'd skip the white (or any contrasting) stitching, though. It'll probably discolor unevenly over time and won't look so nice as it does when new.