Hey, I am a long time lurker and have used this forum a bunch of times for tips and everything. However I have an issue that I would like to ask the greater community for help on.

My situation:
I am on a MPM PE fare from LAX-LHR on Aug 9 returning MAN-LHR-LAX Aug 19. Lucky for me my work has demanded I fly back in the middle of my vacation so I am leaving my wife and son with my family for 3 days in the middle of this trip. To make it up I want to extend my return out 3-4 days (return the 22/23/24). However there is an issue.:

There is MPM availability in PE on the LHR-LAX route (the important one, obviously) but the particular fare class I need on MAN-LHR (N) is not available any day that week. This is despite there being plenty of seats on the planes. I am totally fine not even flying out of MAN and just doing the LHR leg and am even willing to pay them for the privilege of NOT flying me from MAN-LHR. But they can't do this. I have spent upwards of 4 hours on hold with the call centre and the people there are helpful but I sense kind of junior. Since is work is going to be paying for the change fees I have told them I am willing to be charged what ever fees they need to.
Is there any workaround that people here could suggest?