I didn't know this before but Standing Coffee in Noksapyeong has soy milk! It's not written on their menu, but you can just ask the barista.
My caffeine fix: soy cafe latte
Directions to Standing Coffee: Noksapyeong Station, Exit 2. Walk straight and go down to the underpass. When you come up on the other side, take the stairs on the right. Standing Coffee will be on your left.