Definitely not medallion complimentary. Totally not available. Not even Platinum Medallions can get upgraded using PMU's. And I'm 99% certain that you cannot use mileage to upgrade either. Delta upgrade awards are valid only on Delta-operated flights (I presume this is a DL-coded, KE-operated flight, based on where you've posted the question). And Delta does not have upgrade awards with Korean, which wouldn't be available anyway since you've got a DL-coded ticket.

Sorry to bring bad news, but neither option you suggested works. I'm not aware of any other options that would work, under the circumstances.