I ended up putting on some Heidenau Scout K60 tires. They have a reputation for lasting a long time and I ride betrween 50,000 and 80,000 miles a year and I'm tired of changing tires.
I have a tire machine which helps but the rim profile on the GS makes it incredibly difficult to remove and mount tires. If you plan to do it by hand (!) you might want to try it first under ideal conditions.
I still have the Shinkos on hand for emergencies.