i have a fully flex ticket that starts in asia and involves a few carriers, the first 2 segs being BA

i have been able to extend the 3rd flights onwards without any problem,
but trying to get the 2nd flight (which has a sub 24hr lhr stop) has been met with a orbitz answer of $2000 fare diff or BA saying ask orbitz, before you set off , once you start then ask us.

is there any way around this?

do i get on the plane and hope BA will change it once i get to lhr (i have a 6hr wait between flights)