I am traveling in March on KAL economy from JFK to ICN. I have a Delta Skymiles Business AMEX Platinum card as well as being a NWA Worldclubs member. Will either of these gain me access when flying econ to the Morning Calm lounge at ICN?They open at 6:30AM and I will need a shower. My departure flight is at 8, so waiting for the shower facilities to open at ~7AM will make it tight.

Thanks
Tony