My thumb is sore and tender right in between the base and the knuckle. I use it heavily when I play traditional grip. I have been playing a lot more so that may be the culbrit, but I wanted to make sure I wasn't doing anything wrong.
Experiment with drumming off of the index/middle fingers, applying little to no pressure to the thumb. This will allow more of the mass of your hand to become part of the stroke, and will produce a more full sound that is conducive to balancing the right hand.
Also be sure to maintain the connection to your ring finger, since most of the mass of your left hand is actually located under the stick, and this is your one and only connection point under the stick.