Let's suppose that one wants to fly LAX-IAD-LHR rather than LAX-LHR either to have dinner in DC or just for the added FF miles, but that the IAD stop puts one over MPM. One could book a direct flight that connects in IAD e.g. UA924 in the present schedule. Then one could separately make a full fare reservation in the appropriate class of service on an LAX-IAD nonstop which leaves before the LAX-IAD-LHR leaves. One could go to the airport early, check in for LAX-IAD-LHR as ticketed on the RTW getting separate boarding passes for the two segments because you prefer aisle on one and window on the other, then proceed to the gate from which departs the earlier flight. Present only your LAX-IAD boarding pass, tell the agent your travel agent made a reservation on the earlier flight in case you arrived early at the airport, and ask if you can get on the earlier flight.

I don't think there are a lot of cases where this is possible, but it should work in some cases. I haven't actually tried this, but I think it should work. Has anyone tried?