In situations as complicated as this, I've often had good experience with the BA ticketing agents at airport counters - including the transfer desk at LHR.

They'll be able to see that your ticket has been pending for a while - that you didn't irresponsibly leave the change to the last minute. A good agent will take on the challenge, and use whatever GDS jujitsu they can to get you on your way - perhaps even just making an INVOL exchange of the coupons for your next legs, to ensure you won't miss your flights on the day, with follow-up soon thereafter (maybe even while you are in the air) to resolve the more complicated matter of re-issuing the rest.

Good luck.