Craig - I'm thinking mechanics too.

Possibly try changing your letting your arm rock forward a bit from the shoulder and allow your wrist to be a bit further under the neck. That's how I fixed my barre chord problem.

Another possibility, if while playing the G chord you're fretting the high e with your pinky, leave the pinky in place and let the index, middle, and ring go to the C chord. Anchoring your pinky to the third fret may help a bit keeping you grounded. Also, that note happens to be the "fifth" for the C scale so the tone fits.

Hang in there!