Agent69,

OP noted that there were no available seats anywhere on BA59 and no J availability for at least 3 days for both BA and QR. Also given that the Cabin Crew informed OP that they could manually recline the seat (no joy there!) and yes, no room in back. Not knowing OP's status or timings it makes it harder to advise on what they should have pushed for at LHR. Given it was a mechanical issue I probably would have explored routing through AMS with KL through AMS or LH via FRA.

Of course YMMV