I have flipped my stem before, actually going in the opposite direction from that which you want to go. Even though the handling didn't seem to be affected, I would imagine that it does have at least a small bearing. If you flip the stem it may require that the fore/aft position of the seat be changed also. You may also feel more comfortable with the seat nose down a slight amount more with the bars up. My Thomson post with a micro adjust worked great for this. You mention that the front hub is obscured with your hands on the hoods. This is a quick way to tell on most bikes if your stem length is correct, but there are other factors that need to be considered. For instance, on my touring bike, the front hub is obscured when I am on the hoods, but on my road bike I can see a portion of the hub from under the bars. I am more spread out and probably much more aero on the road bike, but I still have bend in my arms and never have back pain even on century rides.