Lisa - interesting that you should mention playing the banjo and stretching your left hand. I have experienced the same thing playing the guitar. I have always struggled with the fact that I have small hands and over the years have tried so many different neck sizes and shapes and been through multiple guitars. My left hand stretches a full inch wider than my right!! I don't think my right hand will ever be too much stronger because I now have a bone spur at the base of my right thumb which isn't too bad when playing the guitar, but is a problem with braking and shifting on the bike. I have Campy, so that helps. I always use full fingered gloves so I can protect my hands. That also seems to help with grabbing the brakes.

Happy riding and playing!!
Nina