I haven't cracked open the gauges yet, but I know my SES is burned out. Is there any way to fix the LED outside of swapping the whole cluster?

 

Yes, just replace the old bulb with a standard or led bulb.
They use bulbs. But, for any light that has an led on it(small square made on to the board), just heat the led leads with a solder gun, and solder on a new led.