Plug it and ride.
I got a flat several miles from home once, no BMW dealer within 300 miles to source a new tire from and there was little chance the Honda shop 30 miles behind me would have a tire for my GS.
So I put a string plug in and rode forward.
Just outside Chadron, Nebraska (some 100 miles later), the string plug failed. So I put two string plugs in and turned around, there was an open auto repair shop in Chadron. Jimmy, who had never seen a BMW motorcycle (nevermind work on one) mounted the wheel in his tire changer, popped a bead off and installed an internal patch. The wheel was buttoned back up and I rode that tire back to Connecticut and replaced it after a couple thousand more miles.
The moral: If a string plug fails, try two. If you're unsure two will hold, the rear wheel of a GS (and likely any BMW) can be mounted in any shop's tire changer and opened up. An internal patch, with the string plug stubs still in place, will last many thousands of miles.
If you're all about the destination, take a fucking flight.