Have you taken out the adjustment screws and pushed the wheel all the way back? That should help. Also which year GS? Older road bikes tend to have better clearance than later ones. Assuming the bike has normal or standard reach (and not short reach) brakes, you can usually find a way to make a 32c tire work.
There are lots of good 32c tire choices out there. Panaracer gravel kings might be a good choice for you given your intended use.