Booked ICN-LOP via CGK in J for 45k miles.

There was a schedule change and now I have a -5 hour layover. I found an acceptable alternative via DPS instead and so I contacted Delta via Twitter and they told me to call Garuda. I called Garuda and they insisted I needed to call Delta. So, I contacted Delta again via phone and was told that there was no inventory available on any routing on my original date of travel. I asked for the agent to contact Garuda’s revenue management to have inventory opened up so the change could be pushed thru, and she said that wasn’t possible.

Any suggestions or relevant past experiences on how to get this resolved?