When you say you want to ride more "efficiently" do you mean you want to roll faster? One thing about your bike, which is similar to mine, is that being more upright means your torso is catching air like wind in a sail. So, although you may go faster with new rims & wheels, not sure you would get what you're looking for. On the other hand it may be just what you like.
I know you said that you hesitate about road bikes, but just to throw it out there-there are many road bikes which are not racing bikes. There are commuting bikes with drop bars. Good luck and let us know what you end up with.