I made it today. 22 minutes riding time. Google maps says it's doable in 18 minutes, but I think they assume that the train pulls into the station just as you get to the platform, rather than leaving as you fret behind the person not walking down the escalator. I left home around 7:20, so I got here at my usual time. Still feel good at 4:00, half an hour before time to head home.
The question now is whether to ride home easy or hard: follow the subway or head up the mountain? I will probably take it easy. I won't necessarily have time to shower right away, and I didn't get to clean up after the morning ride, either, aside from splashing some water on my face.
And it is now time to go. I am hoping to ride back and forth every day this week. Friday I will have to take my bike on the subway, as I have something to do in Haeundae, and not enough time to ride there.