Elk. I have short fingers too.
With my regular drop bars and regular Shimano brake levers on my Rambouillet, i was just barely able to grab my brakes and get two fingertips around them. Those Shimano brake levers do not have shims that are made for them. Not good.
I switched to a short reach bar (Salsa Poco) and that helped a little bit. But still it was scary going downhill fast with just the ends of two fingers barely wrapped around the brake levers. And believe me, I tried putting the hoods in all different places.

Fast forward.....
On my new Luna I again had Salsa Poco bars put on, but this time with Shimano Short Reach brifters (R600 9-speed in my case, R700 for 10-speeders) with their shims installed. OH MAN what a difference. Like night and day. I can get all my fingers nicely gripped around the levers now.
If I were you I would go for it. Juggling bars and angles just didn't cut it for me. On steep downhills it is safer to be braking in the drops.