Some observations I had in recent years: DL does not through check with MU if tickets were booked separately, which results in entering Korea at ICN, getting your luggage, and taking a bus between T1 & T2. This is very time consuming, so through check the luggage is the key for a rapid transfer -- glad to see that this worked out for the OP!

Because of this, I am now only flying KE between PVG and ICN, which offers through check with DL and offers (much) superior service.