Don't know about shuttles, but there is regular bus service from Seoul to Wonji (40 min. from Daewonsa) and from Gurye (30 min. from Seongsamjae) to Seoul.
I'm trying to get shelter reservations, but getting frustrated. I got to credit card checkout the other day, but now, it just rejects my arc outright (actually, without even checking; seems to be a crappy web interface problem).
I guess worst case scenario: go down to the Piagol walk-in shelter, or sneak a bivy.