BJ, I like your idea to rotate the handlebar, or rather rotate the position of your shifters and brakes on the bar. Remember that in your primary riding position there should be no bend in your wrist, rather there should be a straight line from your knuckles up to your elbow. Use that as your guide for setting the rotational position of shifters and brakes.

How about your reach? Is the brake lever within easy reach of your fingers, or do you have to kind of stretch your hand to get to them? If it's a long reach, see if you can adjust the lever closer, or replace the lever with ones that are more adjustable.

It sucks to ride with sore hands. You'll be happy when you fix this!

Hugs and butterflies,
~T~