Good luck. You will need to find a highly experienced agent to be able to do this.
A few years ago I was flying ECP-ATL-MSP-ANC. The ATL-MSP and MSP-ANC legs were both sold out. Late the night before I received a notification my early morning ECP-ATL segment was canceled (late night inbound went missed due to fog). Called up DL to switch to originate out of TLH (a few hours drive, but had availability and I could connect to my originally scheduled ATL-MSP and MSP-ANC flights). I almost got into a screaming match with the agents who kept telling me "No" the second and third segments are sold out. I finally had to explain to them step by step that I was already confirmed on the second and third segments and just needed to change the first. It took escalating to 3 different supervisors to get someone to figure out how to do it. It was finally done, but frustrating. Good luck!