I have a few inputs about your up coming trip to Seoraksan

although i haven't been there, but i'm planning to go there this coming December.
IMO, mahirap mag day tour lang. una, sayang ang punta mo kung mamamadali mo i mean you won't have enough time to enjoy the scenery and linger

2nd, talo ka sa byahe kasi it takes about 5-6hrs ang byahe papunta dun hanggang sa entrance ng Seoraksan. and like what you've said, since mag DIY ka, di kabisado ang lugar may possibility na mas magiging matagal ang pagpunta.
Based sa mga nababasa ko, worth it naman daw ang pagpunta lalo na kung nature lover ka. Sobrang iba daw talaga simoy ng hangin

I'm about to find out this December

keep us posted! goodluck and enjoy!
Info that i got from a website.
From Sokcho or Sokcho Express Bus Terminal, take city bus No. 7 or 7-1 and get off at the entrance of Mt. Seoraksan (30 minute ride).
2. From Sokcho Intercity Bus Terminal, taxi takes 15-20 minute to the entrance of Mt. Seoraksan.