First of all, which fingers go numb? Thumb and forefinger = carpal tunnel syndrome, little and ring finger = something else, the lateral nerve is being inpinged rather than the medial nerve. The reason that I ask is because bicycling gloves are being made to help both conditions. Grandoe makes carpal tunnel gloves, Specialized Body Geometry gloves counter the other condition. Both brands have padding that is designed with spaces so they won't press on the impaired nerves.
How high is your handlebar relative to your seat? If you can find a way to raise your bar, maybe shorten the stem a little, you may be able to avoid having to make more significant changes to your bike.
If you decide to go to a flat bar, mountain bike shifters will work fine with your current derailleurs but you need to get low cable pull brake levers.